Three-Dimensional Hydrodynamic Analysis and Early Warning of Ω-Collapse in the Lower Reaches of the Yangtze River Based on Experimental Study on Generalized Model

Abstract

Under the background of the construction of cascade reservoir group in the main stream of the Yangtze River, the lower reaches of the Yangtze River are faced with new water and sediment situation, which leads to the increased risk of bank collapse in the lower reaches of the Yangtze River. Therefore, the purpose of this study is to have a certain supporting significance for the prevention and control of riverbank collapse disasters. The study takes the Jiangsu section of the lower reaches of the Yangtze River as the research object. Firstly, according to the measured data over the years, the macroscopic characteristics of the collapsed bank in the Jiangsu section are analyzed, and the temporal and spatial distribution characteristics are mainly analyzed. The research results show that the collapse of the Jiangsu section of the Yangtze River is dominated by Ω-collapse, which mostly occurs in the flood season and the post-flood receding water period. The frequency of bank collapse in the Yangzhong Reach is relatively the highest among all river segments, and there are more bank collapses on the north bank than the south bank. According to statistics, the average collapse width of the collapse in the Jiangsu section can reach 130 m, the depth of the collapse can reach 60 m, and the ratio of the average bank collapse to the depth can reach 2.15. Then, aiming at the characteristics of the main bank collapse type in the Jiangsu section is the Ω-collapse, the experimental investigation and numerical calculation are used to conduct in-depth research, combined with the measured data, probability and statistical analysis and theoretical analysis. Three-dimensional hydrodynamic analysis is carried out on the mainstream area near the collapse area and outside the collapse area, focusing on the analysis of its nearshore velocity and shear stress and other factors. Combined with the water tank test, the water flow in the inner surface, middle and bottom layers of the Ω-type nest was studied under different flow levels, and it was concluded that the water flow in the nest had a counterclockwise backflow, and the backflow intensity gradually weakened from the side wall to the center. And the phenomenon that the surface layer and the bottom water flow are separated, and this phenomenon becomes more prominent with the increase of the flow rate.

1 Introduction

The bank collapse patterns in the lower reaches of the Yangtze River can be divided into nest collapse, strip collapse and wash collapse. Nest collapse and strip collapse are the most common forms of bank collapse in the lower reaches of the Yangtze River, with a greater degree of harm. Washing collapse is generally caused by waves, ship waves, etc. with less intensity and less harm, and generally occurs in the estuary area. Collapses mostly occur on the banks of the binary structure. When the height difference of the shoal and groove is large, the nearshore is washed away, the bank slope becomes steep and unstable, and large-scale collapses may occur. Washing avalanche refers to the sliding or slumping of the surface layer of the bank slope or local small-scale soil scoured by water flow, so it is called “washing avalanche”. Strip collapse refers to the collapse of the beach soil with a length of tens of meters, hundreds of meters or even a few kilometers along the direction of the river flow. Strip, so called “strip collapse”. Nest collapse refers to the collapse or collapse of a large area of soil on the river bank or floodplain, and the phenomenon of soil collapse develops into the bank slope. The collapsed soil volume can reach hundreds of thousands of cubic meters, or even millions of cubic meters, and its appearance forms an inwardly concave nest, so it is called “nest collapse”.

The collapsed banks of the Jiangsu section of the Yangtze River are mainly nest collapses. According to incomplete statistics (since 1949, there have been 315 bank collapses of different scales in the Jiangsu section of the Yangtze River. Among them, 191 times of nest collapse occurred, accounting for 60.63% of the total number of collapses, 64 times of strip collapse, accounting for 20.32% of the total number of collapses, including 60 times of washing collapse, accounting for 19.05% of the total number of collapses. It is mainly guarded with the bank slopes of the Jiangsu section of the Yangtze River, and most of its continental beaches are also guarded. The occurrence of strip collapse and wash collapse is relatively small. Due to the large height difference between the riverbed and the beach, the scale of the generated nest collapse is generally large. Therefore, this study conducted an in-depth analysis of the Ω-type nest collapse (Fig. 1).

Fig. 1.

Pie chart of landslide type distribution.

2 Research Progress

River bank collapse is an important subject in the field of river development and governance. From the 1950s to the 1980s, river bank slope erosion was defined as the process of separating, entraining, and transporting river bank soil in the form of particles or aggregates due to water flow and geological action. River bank collapse is defined as partial or complete collapse of the river bank due to soil instability. River bank collapse is the product of the comprehensive action of many factors, including water erosion, seepage erosion, mechanical properties of river bank soil, weathering, etc. Among them, water erosion and seepage erosion will directly lead to the occurrence of river bank collapse. In the mid-1970s, S.frydmom et al. conducted a centrifugal simulation test of river bank instability, and analyzed the soil slip surface and the displacement and strain of the bank slope soil. In the early 1980s, the U.S. Army Corps of Engineers Waterway Test Station began the corresponding experimental and theoretical research work in the lower Mississippi River in the United States. Jingjiang Riverbed Experiment Station, Hankou Hydrological Station and Nanjing Riverbed Experiment Station analyzed the bank collapse of the Jingjiang River, Chenglingji to Jiujiang and Nanjing rivers according to the measured data of the Yangtze River. The main influencing factors are the water flow intensity, the shape of the river bend and the soil conditions of the river bank. Based on the measured data, Yu and Zeng (1986) analyzed the process of forming a “pocket-type” collapse, and believed that for a bend strongly affected by the top-scouring action of the water flow, the near-shore water flow encounters a bank with weaker shock resistance, and it will rush into the bank to form a rotational property. With the strong backflow, with the expansion of the size of the collapsed nest, the river bank eventually forms a “pocket-type” planar shape that is compatible with the backflow intensity.

After the 1980s, Osman and Thorne (1988), Thorne and Osman (1988) and Darby and Thorne (1996), Darby et al. (2015) proposed relatively complete physical models of various bank slope collapses. Osman and Thorne (1988) analyzed the river bed scouring and river bank erosion, and believed that the most common cause of bank collapse was that the lateral erosion process of the river bank widened the river channel and made the bank slope steeper. The ratio reflects whether the river bank is safe or not. On this basis, Darby and Thorne (1996). Added the relationship between the resistance and the dynamic force of the soil, and further analyzed the slope stability. In the 1990s, a number of Dutch scholars also conducted special research on the stability of river bank slopes. Li (1992) analyzed and proposed that the dynamic factor of the collapse of the Nanjing reach of the Yangtze River is the large-scale longitudinal axis (water flow direction) spiral flow. At the same time, the collapse occurs on the river bank with a binary structure where the upper layer of the river bank is sub-clay or silty clay and the lower layer is a silty-fine sand layer, the time is generally high in the flood season. The continuous deepening of the deep groove and the approach to the shore can be used as a condition and signal for the occurrence of the collapse.

At the beginning of this century, Dapporto et al. (2001, 2003) conducted long-term observations on the pore water pressure on both sides of the Sieve River. The river bank of the river is a typical binary structure bank. The observation results found that the variation of matrix suction inside the bank slope is affected by a combination of factors such as seasonal changes, precipitation, flow, evaporation, and changes in the water surface. Huang et al. (2002) pointed out that the main reason for the instability of the beach is the change of the physical properties, state indicators and strength indicators of the soil itself, and introduced the slope stability analysis and seepage calculation methods, and carried out a sensitivity analysis of the main influencing factors. Leng (1993) believes that groundwater movement only inhibits or promotes the collapse of the bank, and the collapse of the lower reaches of the Yangtze River mostly occurs in the post-flood or dry season. Zhang et al. (2006a, b) and others have classified the collapse of the Yangtze River in detail according to the manifestations, failure modes and formation mechanism of the collapse of the Yangtze River. According to the manifestations of the bank collapse of the Yangtze River, the river bank collapse of the Yangtze River is classified into washing collapse, strip collapse and nest collapse, and the characteristics and common river sections of wash collapse, strip collapse and nest collapse are analyzed in detail. Zhang et al. (2006a, b) believes that the process of river bank collapse includes key physical processes such as water flow erosion and seepage erosion. Research by Chen (2000) and others pointed out that the reasons for the collapse of the Yangtze River can be attributed to the infiltration force, the water current scouring the slope foot, the infiltration of the rainstorm into the bank slope soil and the wave dynamic water pressure.

In recent years, with the improvement of computer calculation level, a method of simulating the bank collapse process based on mathematical model calculation has appeared. Xia et al. (2020) combined the plane two-dimensional water and sediment model with the viscous bank collapse mechanics model to simulate the river bank collapse process of the generalized straight reach under different erosion and deposition conditions. Based on the mechanical mechanism of river bank collapse, Jia (2010) deduces and establishes a viscous bank and a dual-structure river bank collapse mechanics model considering the influence of adjacent soil, and establishes a three-dimensional flow and sediment mathematical model to simulate the lateral swing process of the river channel caused by the heterogeneous river bank collapse.

To sum up, there are certain differences in the existing analysis of the causes of river bank collapse in the middle and lower reaches of the Yangtze River, and there is no convincing unified theory for the key influencing factors of river bank collapse, especially the mechanism of collapse. The complexity is directly still not fully understood. Therefore, in this study, the Ω-type nest collapse was studied in depth, and the three-dimensional hydrodynamics and turbulent structure of the collapsed nest were analyzed.

3 Research Method

3.1 Analysis of Bank Collapse Data

The size of the nest collapse is related to the geological conditions of the bank slope, the height difference of the beach and groove, etc. The width of the collapse can reach tens to hundreds of meters, and the depth can also reach tens to hundreds of meters. The average width of the collapse scale in the Jiangsu section of the Yangtze River is about 150 m, and the depth is about 80 m. The typical bank collapse scale of the Jiangsu section of the Yangtze River is shown in Fig. 2.

Fig. 2.

The width of the collapsed door, the depth of the collapse and the ratio distribution.

This study counted the frequency distribution of the width of the mouth of the nest, the depth of the collapse and the corresponding ratios when the collapse occurred since 1949. The results show that the width of the entrance door of the collapsed nest is generally between 50 m–600 m, and the depth of collapse is generally between 10 m–350 m. The average gate width is about 130 m, the average collapse depth is about 60 m, and the median ratio is 2.15. In this physical model experiment, the length of the semi-circular door is 160 m, the width of the collapsed nest is 80 m, and the collapsed nest with a ratio of 2 is used to simulate the collapsed nest, which is in line with the typicality of nest collapse. The selected Ω-type collapsing nests are mainly generalized with reference to typical collapsing nests.

3.2 Analysis of Bank Collapse Data

3.2.1 Model Design

The length of the established test water tank is 40 m, the height is 0.5 m, the width of the water tank is 1.9 m except for the collapsed nest, the radius of the Ω-type collapsed nest is 47 cm, the length of the door is 66.93 cm, and the opening angle is 90°. The axial surface of the collapsed nest is 12.8 m away from the entrance. The upstream of the entire tank is controlled by the water weir, the downstream is controlled by the tailgate, and the slope of the bottom of the tank is 1:1000. A total of 38 measuring points are arranged around the collapsed nest and outside the collapsed nest. The measurement contents of the model test include: water level measurement along the way, three-dimensional flow velocity measurement in the collapse nest and main flow area (Fig. 3 and Fig. 4).

Fig. 3.

Schematic diagram of sink layout.

Fig. 4.

Local map of measuring points in the collapsed nest area.

The three-dimensional flow velocity of the measuring point is measured by the Vectrino Xiaoweilong Acoustic Doppler Point Velocity Meter (ADV) developed by Nortek in Norway. The probe of ADV consists of one transmitting transducer and four receiving transducers. The working principle of ADV is based on the Doppler effect. The transmitting transducer sends out a pulse signal of a certain frequency, and the flow velocity information is obtained by measuring the phase difference of the pulse signal by the receiving transducer. The flow velocity measuring point is 5 cm away from the transmitting transducer, the sampling frequency is 25 Hz, and the accuracy is ±1 mm. The ADV probe has two forms, one is a downward-looking probe, and the other is a side-looking probe. This test uses a downward-looking probe for measurement.

3.2.2 Model Parameters

Referring to the nearshore flow velocity and water depth conditions of the natural bank collapse risk section of the Jiangsu section of the Yangtze River, considering that the natural water depth is generally 20–40 m, and the flow rate is 1.5–3 m/s, the combination of water depth and flow rate is selected as the selection range of the fixed bed test. The model similarity conditions are as follows:

• It is necessary to meet the gravity similarity criterion and the resistance similarity requirement at the same time.

• Flow rate scale: $\lambda_{u} = \lambda_{h}^{1/2}$

• Flow scale: $\lambda_{Q} = \lambda_{h}^{5/2}$

• Time scale: $\lambda_{t} = \lambda_{h}^{1/2}$

• Roughness scale: $\lambda_{n} = \lambda_{h}^{1/6}$

• The turbulence limiting conditions and the surface tension limiting conditions must be met.

• $Re_{m} > 1000\;{\text{and}}\;h_{m} > 1.5\,{\text{cm}}$

• The scale chooses $\lambda_{h} = \lambda_{l} = 100$, then $\lambda_{u} = 10,\lambda_{n} = 2.1544.$

The test groups are as follows (Table 1):

Table 1. Test groups.

4 3D Hydrodynamic Model Study

4.1 The Distribution Characteristics of Plane Velocity and Flow Field in the Collapse Nest Area

Based on the results of the water tank model test, the plane flow velocity and flow field distribution in the Ω-shaped collapse nest were analyzed, and the water surface ratio was 0.96‰ under heavy water conditions. Under various water flow conditions, the water surface line is slightly high at the entrance of the collapsed nest, which is because the backflow in the collapsed nest area at the entrance merges into the main flow and causes local stagnant water (Fig. 5).

Fig. 5.

Variation diagram of water surface line along the route.

Figure 6 is the test site map of the collapsed nest area under three water flow conditions. The surface velocity distribution is observed by using paper flowers. The surface velocity distribution under the three water flow conditions is basically similar, and there is a counterclockwise movement along the side wall near the collapsed nest. In the center of the collapsed fossa, there is a slow flow area, and there is a local vortex in a long transition area near the mouth.

Fig. 6.

Test site map of the collapsed nest area.

Figure 7 and Fig. 8 is the flow velocity distribution diagram of the water tank test. Under the condition of high water, the flow velocity of the upper and lower sections of the collapsed nest and the outer area of the collapsed nest is about 0.26–0.33 m/s. The internal velocity of the collapsed nest increases with the distance from the center of the collapsed nest. The flow velocity at the side wall and the mouth of the collapsed nest is about 0.1–0.13 m/s, which is about 40% of the velocity of the upper and lower sections of the collapsed nest and the outer area of the collapsed nest. The flow velocity in the external area is about 0.21–0.26 m/s, and the inside of the collapsed nest is still the largest at the sidewall and the mouth of the collapsed nest, between 0.09–0.11 m/s, which is about the upper and lower sections of the collapsed nest and the outside of the collapsed nest. About 43% of the regional flow velocity, the flow velocity of the upper and lower sections of the collapsed nest and the outer area of the collapsed nest is about 0.15–0.19 m/s under small water conditions, and the flow velocity at the side wall and the mouth of the collapsed nest is between 0.06–0.07 m/s. It is about 39% of the flow velocity of the upper and lower sections of the collapsed nest and the outer area of the collapsed nest. It can be seen that the flow velocity at the inner wall of the collapse nest is generally about 40% of the flow velocity in the mainstream area. Figure 9 shows the relationship between the flow velocity in the mainstream area and the flow velocity near the wall of the collapsed nest under the condition of three water flows. Combined with the results of Yu and Su (2007) measured in the collapsed nest area at Yangzhou Port, the correlation between the flow velocity in the mainstream area and the maximum flow rate in the collapsed nest is calculated. The fitting of the relationship shows that the linear relationship is better, and the regression coefficient can reach 0.95. For the axial plane of the collapsed nest, the size of the external and anterior and posterior sections of the collapsed nest is basically similar, but slightly different. The flow velocity into the collapsed nest decreased sharply, and the flow velocity approached to zero at the center of the collapsed nest. Although the flow direction was opposite to the side wall, the flow velocity gradually increased. The flow velocity inside the collapsed nest basically presents a “V”-shaped flow velocity distribution, and the flow velocity at the top of the bend is basically the same as the flow velocity at the mouth, and the flow direction is opposite.

Fig. 7.

Velocity distribution in the collapsed nest area.

Fig. 8.

Distribution of flow field in the collapsed nest area.

Fig. 9.

The relationship between the flow velocity in the main flow area of the Ω-type nest collapse and the maximum flow velocity near the wall in the collapse nest area.

4.2 Distribution Characteristics of Vertical Flow Velocity in the Collapse Nest

Figures 10 are the flow field diagrams of the vertical velocity distribution at the surface, middle and bottom layers at the side wall of the collapse nest under three water flow conditions. Under high water conditions and under moderate water conditions, the difference in the flow velocity of the middle and bottom layers near the wall of the collapse nest is basically very small, and the flow direction near the wall is shown in Fig. 10. The flow rate of the middle bottom layer basically follows the boundary of the collapse nest, and the surface flow velocity appears obvious in some areas. The vertical flow velocity of the stratification is significantly larger than the flow velocity of the middle and bottom layers, and its direction is always biased towards the side wall direction, and has a normal sub-velocity relative to the side wall. Through analysis, the phenomenon of separation of flow velocity in the middle and bottom of the table is basically collapsed. On the chord of the nest (ie from 45° to 225° relative to the center of the collapse), the dispersion of the vertical flow velocity will cause brushing at the side walls of the collapse. This is because the stronger the separation characteristics of the surface and the bottom layer of the water flow, the more conducive to the diffusion and energy consumption, causing scouring, and there is a secondary backflow.

Fig. 10.

Distribution of vertical stratified flow velocity in the collapsed nest area.

Figure 11 establishes the relationship between the relative deflection angle and the flow velocity of the bottom layer of the collapsed nest under the condition of reclaimed water. Combining with Fig. 10, it can be seen that when the water flow enters the collapsed nest (that is, after passing through 7#-2 and 8#-3), the flow rate begins to decrease. But the flow velocity is still at a relatively large level in the collapse nest, and the surface and bottom declination angles of about 8° and 5° are generated. It enters the collapse nest and continues to the vicinity of 8#-1, and the flow velocity continues to decrease. There is no obvious deviation from the bottom layer of the surface, and the deflection angle is only about 1°. The water flow velocity fluctuates along the process from 7#-1 to 2#-3. The flow velocity is relatively large at 0.1–0.13 m/s, and the declination angle of the surface and bottom water flow is relatively large and basically between 15–45°. The above shows that the water flow inside the collapse nest exists with the increase of the flow velocity during the swirling motion. The factor of water flow diffusion and energy consumption, under the action of water flow diffusion, the risk of digging and brushing of the side wall of the collapsed nest increases.

Fig. 11.

The relationship between the relative deflection angle of the surface and bottom flow velocity of the collapse nest and the flow velocity.

4.3 The Distribution Characteristics of Turbulent Kinetic Energy and Shear Stress in the Collapsed Nest Area

Turbulence kinetic energy is the kinetic energy possessed by fluid turbulence, and is an important indicator to measure the degree of water turbulence. Except for a small part of the turbulent energy that is directly dissipated as heat energy due to viscous deformation in the mainstream area, most of the turbulent energy is transferred to the near-wall area through shear force, and converted into turbulent kinetic energy there. A vortex with a certain size and rotation speed is generated and rises into the mainstream area, and the vortex decomposes and transfers energy step by step until the vortex is so small that the viscous effect dominates, and finally it is dissipated as heat through the viscous deformation of the water flow. It is this part of the energy that makes the turbulent flow diffuse and forms a special shear field to suspend the sediment. The calculation formula of turbulent kinetic energy k_T is as follows:

$$ k_{T} = \frac{1}{2}\left( {\overline{{u^{\prime 2} }} + \overline{{v^{\prime 2} }} + \overline{{w^{\prime 2} }} } \right) $$

(1)

where u′, v′, w′ are the velocity fluctuations in the x, y, and z directions after the flow velocity undergoes Reynolds decomposition.

Three different kinds of water flow conditions under the disorder kinetic energy as shown in Fig. 12 (unit cm²/s²), the turbulent kinetic energy of the mainstream area under large water conditions is generally about 2, the near wall of the collapse nest is at entrance and exit and in the lower part of the mouth. The turbulence kinetic energy is significantly higher than that of other near the wall, generally above 10 cm²/s², the reclaimed water condition is similar to the water, the disorder kinetic energy of the mainstream area is generally about 2 cm²/s², and the near wall of the collapse nest is at the entrance and exit and in the lower part of the mouth. Regional disorder kinetic energy is significantly higher than other near-wall, generally above 4 cm²/s², under small water conditions and the former is slightly different, the turbulent kinetic energy of the flow zone is generally about 2 cm²/s², but at −30° the disorder kinetic energy is large, can reach more than 10 cm²/s².

Fig. 12.

Turbulent kinetic energy distribution under different flow conditions.

Shear stress is the most intuitive expression reflecting the action of water flow. In this study, the shear stress was solved by the turbulent kinetic energy method. The three-dimensional turbulent kinetic energy method, also known as the turbulent energy method, uses the fluctuating flow velocity in three dimensions to calculate the bed shear stress. Its formula is as follows:

$$ \tau_{b} = C_{1} \rho 0.5\left( {\overline{{u^{\prime 2} }} + \overline{{v^{\prime 2} }} + \overline{{w^{\prime 2} }} } \right) $$

(2)

where τ_b is the turbulent shear stress, C₁ is an empirical constant, generally taken as 0.19, McLelland and Nicholas (2000) uses a new method to calculate the total measurement error for the inherent error of ADV measurement, which mainly includes sampling error, ADV noise, and single-point ADV caused by shear flow velocity. The error between the relevant sampling quantities is measured, and the results show that the ADV can characterize the turbulent velocity at the frequency of the maximum sampling rate with very small error. Therefore, it can be considered that the position close to the bed surface is measured by ADV, and the shear stress calculated from the obtained data is the bed surface shear stress. The distribution of small turbulent shear stress for three different water flow conditions is similar to the distribution of turbulent kinetic energy.

5 Conclusions

In this study, the Ω-type nest collapse was studied by using technical methods such as field investigation, theoretical analysis, probability and statistical analysis, and generalized water tank test. The main conclusions are as follows:

• 1. There is a circulation that moves counterclockwise along the side wall in the collapsed nest area, while in the center of the collapsed nest is a slow flow area, and there is a local vortex in a long transition area near the mouth. For the axial plane of the collapsed nest, the flow velocity into the collapsed nest decreases sharply, and the flow velocity at the center of the collapsed nest has approached zero, and the flow direction near the side wall is reversed, but the flow velocity gradually increases. The flow velocity inside the collapse nest basically presents a “V”-shaped flow velocity distribution, and the flow velocity at the top of the bend is basically the same as the flow velocity at the mouth, and the flow direction is opposite. The backflow in the collapsed nest area at the entrance merges into the main stream, causing local backwater and raising the water surface line. The flow velocity at the inner wall of the collapse nest is generally about 40% of the flow velocity in the mainstream area.

• 2. The vertical flow velocity inside the collapse nest will be inconsistent in direction. The phenomenon of separation of flow velocity at the bottom of the table is basically the upper string of the collapse nest (that is, the area from 45° to 225° relative to the center point of the collapse nest). The dispersion of the vertical flow velocity will cause brushing at the side walls of the collapsed nest. When the water flow inside the collapsing nest is doing gyratory motion, there is a factor of water flow diffusion and energy consumption with the increase of the flow velocity.

• 3. Under the conditions of high water and medium water, the turbulent kinetic energy of the near wall of the collapse nest at the inlet and outlet and the attachments at the lower part of the mouth door is significantly higher than that of other near walls. The shear stress distribution has a good positive correlation with the turbulent kinetic energy distribution.