Keywords

1 Introduction

From the perspective of fluvial evolution, bank collapse is the movement of a large number of sediment particles under the interaction between the river flow and the river bed boundary, which is caused by the unbalanced sediment transport (Yang et al. 2022). River bank collapse is widespread and is a natural disaster with great harm (Kimiaghalam et al. 2015) For the Heilongjiang River in Northeast, the main trunk reaches are important boundary rivers in our country, and the erosion of banks and beaches will directly cause the loss of farmland (Jia et al. 2021). There are significant differences in the process, and the characteristics of freezing and thawing are obvious. Therefore, it is of great theoretical significance and practical guiding value to carry out research on the collapse of river banks and beaches in seasonally frozen regions.

For the problem of bank collapse, its formation mechanism and occurrence process are complex, and the existing research cannot fully reveal its evolution law. In response to such problems, many experts and scholars at home and abroad have carried out research on the mechanism of bank collapse, revealing different influencing factors of river bank collapse. At the same time, many scholars have constructed different collapse modes based on the theory of soil mechanics slope stability. Calculation model of river bank stability under. For example, in terms of revealing the influencing factors of river bank collapse analyzed the influence of curved circulation on bank erosion and its change process(Papanicolao et al. 2007). The interaction process of bank slope collapse and river bed erosion and deposition is also analyzed (Yu et al. 2016). The existing riverbank stability analysis models are usually based on the slope stability theory in soil mechanics. considered the influence of pore water and hydrostatic pressure, and made corresponding supplements and improvements to the previous viscous bank collapse model (Darby et al. 1996). However, such simulations do not take into account the effect of the freezing and thawing of seasonally frozen rivers, so further improvement is needed.

This paper takes the typical dual-structure bank of the Songhua River as the research object, considering the freezing and thawing of soil, lateral water pressure, and combining with the slope toe scour calculation module, the typical section near the dam in the downstream of the Dadingzishan Aviation and Power Project of the Songhua River is taken as the research object. Taking a river bank as an example, the BSTEM model was used to calculate the river bank stability in different periods of the entire hydrological year in 2009, and to analyze the change process of the corresponding safety factor Fs.

2 Materials and Methods

2.1 Study Area

The Songhua River is one of the seven major rivers in my country and the largest tributary on the right bank of the Heilongjiang River. The main stream of the Songhua River has a well-developed water system. There are many tributaries along the way. The main stream of the Songhua River is a typical plain alluvial river, with a total length of about 940 km and a catchment area of 186,400 km2. Except for the hills and hills in the middle part, it is basically an alluvial plain. According to the terrain, topography and river nature, the main stream of the Songhua River can be divided into three sections: upper, middle and lower reaches. The vegetation in the basin is rich in humus. The surface layer on both sides of the river channel is black humus soil, 0.5–1.5 m below the surface layer is clay or sandy clay, the lower layer is silt or fine sand, and the river bed is composed of medium-fine sand and sandy loam. Composition, loose texture and poor impact resistance.

The phenomenon of river freezing is very common in the high latitudes of northern my country, among which river freezing can be divided into stable freezing and unstable freezing. Heilongjiang and its tributaries, Songhua River in the Northeast, due to the dominant low temperature in winter, although there is a large flow and flow rate in the river, it is frozen every year, which is a stable freezing, and the freezing period is generally 4 to 5 months. Therefore, such rivers are also called seasonally frozen rivers, or “seasonally frozen rivers” for short. For the non-freezing period (free flow period), the movement of water and sediment in the seasonally frozen area and its channel evolution are basically the same as those of conventional rivers. However, during the freezing and thawing period of the river, the physical and mechanical properties of the bank soil will change, and the river bank will be stable. Sex is also further affected.

The calculated section of the selected river section is located near the dam downstream of Dadingzishan Avionics Junction. The Dadingzishan Avionics Junction project started construction in 2004 and was put into use at the end of 2008. It is the eighth part of the overall plan for the cascade development of the Songhua River Channel One of the hubs. The operation of the junction and the reduction of upstream sediments have caused obvious erosion in the downstream section of the dam near the dam, deep groove swings, and beach avalanches occur from time to time.

2.2 Numerical Modeling

The BSTEM (bank stability and toe erosion model) model developed by the National Sediment Laboratory of the United States can simultaneously consider the effects of lateral water pressure, pore water pressure, soil matrix suction and different compositions of river bank soil layers. The scour and bank stability model simulates the process of bank collapse and is one of the most widely used models.

The model is mainly composed of the toe scour module (TEM) and the bank stability module (BSM). By inputting the typical river bank profile topography, channel water level, soil physical and mechanical parameters, etc., run the slope toe scour module and import it into the bank stability module to calculate the bank stability safety factor Fs according to the new terrain after scour.

2.3 TEM Modle

The lateral scour width acting on the bank soil is determined by the lateral scour rate and scour time of the river bank. Among them, the lateral scour rate of the river bank is mainly determined by the scour strength of the water flow and the scour resistance of the soil body. Only when the shear stress of the near-shore water flow applied to the river bank soil body is greater than the starting shear stress of the river bank soil body, the river bank soil body can start. The lateral scour width E (m) of the river bank is expressed as:

$$ E = k \cdot \left( {\tau_{f} - \tau_{c} } \right) \cdot t $$
(1)

where \(E\) = erosion distance (m), \(k\) = erodibility coefficient (m3/N s), \(\Delta t\) = time step (s), \({\tau }_{f}\) = average boundary shear stress (Pa), and \({\tau }_{c}\) = critical shear stress (Pa).

2.4 BSM Modle

The BSTEM model uses the limit equilibrium method to calculate the bank stability safety factor Fs, including the horizontal layer method, the vertical slice method and the cantilever shear collapse method. The main calculation formula of the stability safety factor is:

$$ F_{s} = \mathop \sum \limits_{i = 1}^{I} \left( {c_{i}^{^{\prime}} L_{i} + \left( {\mu_{a} - \mu_{w} } \right)_{i} L_{i} \tan \varphi_{i}^{b} + \left[ {W_{i} \cos \beta - \mu_{ai} L_{i} + P_{i} \cos (\alpha - \beta )} \right]\tan \varphi_{i}^{^{\prime}} } \right)/\mathop \sum \limits_{i = 1}^{I} \left( {W_{i} \sin \beta - P_{i} \sin [\alpha - \beta ]} \right) $$
(2)

where ci′ = effective cohesion of ith layer (kPa); Li = length of the failure plane incorporated within the ith layer (m); Wi = weight of the ith layer (kN); Pi = hydrostatic-confining force due to external water level (kN/m) acting on the ith layer; b = failure-plane angle(degrees from horizontal); a = local bank angle (degrees from horizontal); and I = number of layers.

2.5 Field Data

  1. (1)

    soil properties In order to obtain the calculation parameters of the soil composition and mechanical properties of the river bank required by the model, a field investigation was carried out on the typical section of the bank collapse, and layered sampling was carried out according to the composition, structure and properties of the soil at the section., according to the “Standards for Geotechnical Test Methods” (GB/T50123–2019), the shear test of the soil sample is carried out, and the shear strength of the corresponding soil body is obtained. The physical and mechanical properties of the riparian soil are shown in Table 1.

    Table 1. Parameters for the bank soil properties at sections of DM1
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  2. (2)

    Flow changes The annual average precipitation in the Songhua River Basin is generally around 500 mm. The precipitation from June to September in the flood season accounts for 60% to 80% of the whole year, and the precipitation from December to February in winter is only about 5% of the whole year. The model water level process during the simulation period is shown in Fig. 1.

    Fig. 1.
    figure 1

    Water level processes of model

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3 Results and Discussion

In order to analyze the stability of the river bank in different periods, considering the effect of freezing and thawing, a typical section of DM1 at a distance of 3 km downstream of the Dadingzishan Aviation and Power Junction of the Songhua River was selected to calculate the river bank stability. According to the initial measured river bank shape, the hydrodynamic conditions at the cross section and the mechanical properties of the soil, the BSTEM model was used to calculate the stability of each period, and the change process of the corresponding safety factor Fs was obtained, as shown in Fig. 2, 3 and 4 The calculation results are as follows:

  1. (1)

    During the dry season (12.15–3.15), the discharge flow of Dadingzishan Reservoir is relatively small and does not change much. The average water level through this section is less than 108.5 m, the water level in the channel is low, and the shear stress of near-shore water flow is relatively small. It is smaller, but still greater than the starting shear stress of the lower sandy soil layer. At this time, there is a certain scour in the lower sandy soil layer of the binary structure river bank. According to the calculation and statistics, the scouring amount of the slope foot in the dry season in 2009 was 13.87 m3·m−1; however, due to the gentle slope of the river bank and the small pore water pressure in this period, the river bank has a high degree of stability, and the stability safety factor Fs value is correspondingly large. The average Fs value is basically above 1.8, and the probability of bank collapse is very small.

  2. (2)

    During the Level rising stage (3.16–5.31), the ice melts, the flow will increase accordingly, the water level in the river channel will rise, and the sandy soil layer on the lower part of the river bank will be further eroded. According to statistics, the scour amount of the sections in 2009 was 6.77 m3·m−1, and the value of the stability safety factor Fs was relatively small at this time. The existence of freeze-thaw effect affects the shear strength of soil, resulting in the reduction of river bank stability. According to the calculation and statistics, the Fs value of the section at this time has dropped to about 1.32. In fact, during the freezing and thawing period around the beginning of April every year, a unique spring flood phenomenon will occur in a short period of time, and the resulting ice will also adversely affect the stability of the bank. In the situation, there is still the possibility of bank collapse during the rising water stage before the flood season. It belongs to the stage with strong shore collapse intensity.

  3. (3)

    During the flood period (6.1–10.31), the flow in the river channel increases, the water level reaches the highest level in the whole year, the sandy soil layer in the lower part of the river bank is washed away, the bank slope becomes steep, and the water level in the river channel rises and falls during the flood peak period, and the diving level rises steadily, resulting in higher pore water pressure and lower overall bank stability. According to the calculation and statistics, the scour amount during the flood period in 2009 was 11.18 m3·m−1, and there was1 collapse, and the collapse amount was 26.06 m3·m−1. In general, during the flood period, the toe of the slope has the most severe erosion, the largest amount of collapse, and the poor stability of the river bank, which is the stage of frequent bank collapse.

  4. (4)

    During the Recession stage (11.1–12.15), the water level in the river channel drops rapidly. As the water level decreases, the lateral water pressure acting on the river channel gradually decreases. As the angle increases, the safety factor decreases, increasing the possibility of river bank collapse. During the calculation process, the scour amount during the flood period in 2009 was 5.09 m3·m−1, and 1 collapses occurred, and the collapse amount was 16.75 m3·m−1; from this section, the scour amount during the 2009 flood period was less, but the collapse occurred large amount. It shows that through the cumulative effect of previous water current scouring and freeze-thaw effects, the possibility of bank collapse during the receding period is high, which belongs to the stage of frequent bank collapse.

Fig. 2.
figure 2

Safety factors of bank satiability during different stages

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Fig. 3.
figure 3

Calculated bank erosion and failure volumes under different stages

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Fig. 4.
figure 4

Changes of bank profiles at different stages

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4 Conclusions

Taking the typical section of the bank near the dam downstream of the Dadingzishan avionics project on the Songhua River as an example, considering the effect of soil freezing and thawing, combined with the scouring of the slope foot, the BSTEM model was used to calculate the river bank stability in the whole hydrological year of 2009, and quantitative analysis of the freezing and thawing effect was carried out. The effect of melting on river bank stability. The main research conclusions are:

  1. (1)

    The stability of the bank in different periods of the typical dual structure river bank was calculated, and the results showed that the soil loss of the DM1 section in the dry period and the flood period was dominated by the erosion of the slope foot, and the collapse amount in the flood period and the receding period accounted for the majority. About 54% of the total scour and collapse volume is dominated by river bank collapse during this period.

  2. (2)

    The river bank stability is relatively high in the dry and high water periods; the river bank stability is relatively low in the flood period and the receding water period, with 2 collapses in total, which is a period of frequent bank collapses.

  3. (3)

    Taking into account the scouring of the slope toe, the effects of freezing and thawing, the stratification of soil mass and the accumulation of soil mass at the toe of the slope after the collapse, etc., the typical binary structure river bank was simulated, and the change of the bank safety factor Fs in the whole hydrological year was obtained. The simulation results of the river bank collapse law are in good agreement with the actual collapse results. The simulated method of river bank and beach collapse in seasonally frozen areas considering the effects of freezing and thawing provides an effective idea for in-depth study of river bank and beach collapse in seasonally frozen areas and its management of river banks.