A method to overcome the scale effect problem in local scour physical experiments of underwater structures

Abstract

The present invention belongs to the research field of marine engineering, ports, coasts and offshore engineering, and proposes a method to overcome the scale effect problem of physical experiments on local scour of underwater structures, and accurately predict the local scour of underwater structures. Based on the apparent scour rate of soil, the present invention establishes a method for accurately predicting the local scour of underwater structures, effectively overcoming the scale effect problem of physical experiments on local scour of sediment; it is suitable for the prediction of local scour of any structural form under any sediment type conditions; the present invention transforms the problem of local scour of sediment of underwater structures into a traditional marine engineering hydrodynamic problem. The present invention can take into account the changes in flow conditions over time and the changes in flow direction, which cannot be considered in previous local scour analysis and prediction models. The method proposed by the present invention can be directly applied to research fields such as local scour prediction of underwater structures, in-situ stability, and design of anti-scour measures.

Description

Technical Field

[0001] The invention relates to the research fields of ocean engineering, ports, coasts and offshore engineering, and in particular to a method for overcoming the scale effect problem of local scouring physical experiments of underwater structures. Background Art

[0002] Under the action of fluid flow, various underwater structures, such as submarine cables, fixed wind turbine foundations, underwater production systems, fixed offshore oil platform foundations, etc., are very likely to induce serious local scouring around these structures, resulting in instability and damage of the structures in situ, causing huge economic losses and environmental disasters. Therefore, many scholars at home and abroad have carried out a lot of research on the problem of local scouring of underwater structures.

[0003] The local scouring of underwater structures involves a strong nonlinear interaction between fluid, structure and seabed, and this physical process has obvious three-dimensional characteristics. For the study of local scouring of underwater structures, numerical simulation faces a huge challenge of large computational complexity, and it is difficult to obtain the scouring and deposition characteristics of underwater structures in a short time. In addition, numerical simulation is usually carried out in the mode of fluid flow + turbulent closed model + sediment transport, and the relevant sediment transport models (bedload and suspended load transport) are all established on the basis of loose and uniform sand. The seabed sediments in my country's offshore waters are mainly silty and silty. Compared with loose and uniform sand (without viscosity effect), these seabed sediment forms often have very different starting conditions and transport characteristics, which makes the numerical prediction of scouring for prototype underwater structures produce large errors. Therefore, the current research on local scouring of underwater structures mainly relies on indoor physical experiments. However, due to the limitations of the size of laboratory sinks or pools, the prototype underwater structure must be geometrically scaled to carry out physical experiments. Therefore, the relevant physical experimental results will inevitably be affected by the scale effect of the model. The scale effect of the model is mainly reflected in the following aspects: 1) There are many parameters that affect the local scouring of underwater structures. Currently, no similarity law can meet the similarity requirements of all physical parameters; 2) Sediment particles cannot be scaled according to the geometric scale, otherwise it will lead to significant changes in the physical and mechanical properties of sediment, making the experimental results distorted. Therefore, the current physical experiments on local scouring of underwater structures are all skewed; 3) The current local scouring of underwater structures basically only considers Froude similarity and ignores Reynolds similarity. This is mainly because Froude similarity and Reynolds similarity are naturally contradictory and cannot be satisfied at the same time. In fact, the Reynolds number will profoundly affect the flow state around the structure, and then affect the local scouring of the foundation; 4) The accuracy of the current physical experimental results extrapolated to the prototype strongly depends on the selection of the main control variables. In fact, the parameters that affect the local scouring of underwater structures are interrelated and coupled, and they jointly determine the scouring characteristics around the underwater structure, which makes the selection of the main control variables more difficult. The above factors lead to large errors in the results of laboratory physical experiments when extrapolating to prototypes, and the errors are difficult to quantify. They may even cause different researchers to produce very different results when modeling and extrapolating local scour of the same prototype underwater structure. These factors greatly limit the engineering application value of laboratory physical experiment results.

[0004] In addition, many scholars have not considered the scale effect in local scour physical experiments. Instead, they have established relevant empirical prediction formulas for specific underwater structures based on the induction, summary and analysis of the observation results of a large number of physical experiments. They are directly used for the prediction of local scour of underwater structures. Taking the underwater vertical cylindrical structure as an example, the empirical prediction formula for the equilibrium scour depth under the action of unidirectional flow is as follows:

[0005]

[0006] In the above formula, S c It represents the equilibrium scour depth of a vertical cylinder under unidirectional flow, and D represents the diameter of the vertical cylinder. The formula for the local scour equilibrium depth of a vertical cylinder under wave action is as follows:

[0007]

[0008] Among them, S w Indicates the equilibrium scour depth of a vertical cylinder under wave action, KC = U w T / D represents the Keulegan-Carpenter number, U w represents the amplitude of the velocity of water particles outside the wave boundary layer, and T represents the wave period. The effective range of this formula is KC ≥ 6. The main reason is that when KC < 6, the horseshoe vortex in front of the cylinder cannot be formed, and the horseshoe vortex is the root cause of local scour of the cylindrical structure. At this time, local scour will not occur.

[0009] For the local scouring problem of vertical cylinders under the combined action of waves and currents, the following empirical formula can be used to predict the equilibrium scouring depth:

[0010]

[0011] Where S represents the local scour equilibrium depth of the vertical cylinder under the combined action of waves and currents; A and B are constant coefficients, which can be calculated using the following formula:

[0012]

[0013] Among them, U cw =U c / (U c +U w ), U c Indicates the flow rate of unidirectional flow.

[0014] It should be noted that the above empirical prediction formulas are all for predicting the local scour equilibrium scour depth of underwater vertical cylinders, but these formulas are only applicable to specific structural forms and are not universal. In addition, these formulas are all based on loose and uniform sand in the laboratory and cannot take into account the transport characteristics of clay soil at the engineering site. Therefore, their prediction accuracy and scope of application have certain limitations.

[0015] In summary, the current prediction methods for local scour of submarine structures have certain limitations, especially physical experiments cannot overcome the scale effect problem and cannot accurately consider the transport characteristics of clay at the engineering site, resulting in high uniformity of prediction accuracy. Therefore, it is urgent to develop a new engineering prediction method for local scour of submarine structures, overcome the scale effect problem of physical experimental models for local scour of sediment, form an objective and accurate engineering extrapolation method, and accurately predict the scouring and deposition characteristics of various underwater structures, thereby providing a scientific basis and technical guarantee for the design, safe operation and maintenance of various underwater structures. Summary of the invention

[0016] In order to solve the above-mentioned problems existing in the prior art and meet the practical needs of scour assessment and in-situ stability design of underwater structures, the purpose of the present invention is to provide a method to overcome the scale effect problem of local scour physical experiments of underwater structures, thereby effectively overcoming the scale effect problem of sediment physical experiments, and providing scientific basis and technical guarantee for the local scour analysis and prediction of submarine structures, in-situ stability design and anti-scour measures. This method starts from the physical nature of local scour, that is, no matter what type of underwater structure, what characteristics of seabed sediment (soil), the physical nature of local scour of the structure is that the shear stress τ of the seabed around the structure is greater than the critical shear stress τ of the soil. cr By applying this method, the local scour development process of underwater structures and the scour equilibrium profile can be accurately predicted, thereby effectively overcoming the scale effect problem of local scour physical experiments.

[0017] The technical solution of the present invention is as follows: A method for overcoming the scale effect problem of a physical experiment of local scouring of an underwater structure comprises the following steps:

[0018] Step A: Establishing different sediment transport characteristics formulas

[0019] Regardless of the form of underwater structure, the development process of local scouring is closely related to the characteristics of the soil, specifically, including the soil transport rate, transport mode (bedload transport, suspended load transport, bedload and suspended load combined transport) and the critical starting stress of the soil. For actual engineering, due to the relatively complex characteristics of the soil, there is currently no unified formula to describe it. It is necessary to carry out physical experiments on the apparent scouring rate of the soil to obtain the quantitative relationship between the apparent scouring rate of the soil and the shear stress of the seabed under different flow conditions and the critical starting stress; by carrying out physical experiments on the apparent scouring rate of the soil under different flow conditions, a prediction formula for the apparent scouring rate of the soil is established:

[0020] χ=σ(τ c -τ cr ) ε (5)

[0021] Among them, χ represents the apparent scour rate of soil, which represents the scour depth of soil without structure under certain flow conditions per unit time; σ and ε are constant coefficients, which are obtained by fitting the data obtained from the physical experiment of apparent scour of soil by the least square method. The two constant coefficients represent the transport capacity of soil; τ cr It represents the critical shear stress of the soil, characterizes the soil's anti-scouring ability, and is an inherent property of the soil; τ c It represents the seabed shear stress caused by fluid flow, which represents the shear capacity of fluid on the soil on the seabed and is also the fundamental reason for scour. c >τ cr When the soil is transported, scouring occurs; the seabed shear stress is obtained by analyzing the velocity profile obtained by measurement. Under the action of the fluid, the distribution of the horizontal velocity in the depth direction conforms to the following logarithmic rate distribution:

[0022]

[0023] Where U(z) represents the horizontal velocity measured at height z, κ = 0.4 represents the Karman constant coefficient, z0 represents the seabed roughness height, and the median particle size d of the seabed sediment is 50 The calculation method is z0=d 50 / 12, u* represents the bottom friction velocity; when the velocity at a point in space is known, the bottom friction velocity can be calculated using formula (6);

[0024] When the sea condition is a unidirectional flow, the seabed shear stress τ in formula (5) is c The following formula is used for calculation:

[0025]

[0026] Where ρ represents the density of water. For the critical shear stress of soil in formula (5), the calculation method is as follows: when χ=10 -7m / s, the method for analyzing the critical shear stress of soil is also applicable to the flow conditions of wave and wave-current combined action (Roberts J., Jepsen R., Gotthard D., Lick W., 1998. Effects of particle size and bulk density on erosion of quartz particles. J. Hydraul. Eng., 124 (12): 1261–1267.); for the transport rate formula of soil under the combined action of wave and wave-current, its form is consistent with formula (5), and its core is also to obtain the seabed shear stress in formula (5). For the calculation and analysis method of seabed shear stress under wave action, please refer to the work previously carried out by the applicant of the present invention (Teng, YF, Lu L., Cheng L., Tong FF, Tang GQ, 2022. A modified defect function for wave boundarylayers. Coast. Eng., 171: 104050), when the wave height, period and median particle size d of seabed sediment are known 50 , select the velocity profile when the boundary layer is fully developed, and then calculate the seabed shear stress τ caused by wave conditions using formulas (6) and (7): c As for the combined action of waves, the seabed shear stress caused by it can be obtained by analyzing the seabed shear stress caused by unidirectional flow and the seabed shear stress caused by wave conditions respectively, and the seabed shear stress caused by the combined action of waves and currents can be calculated by linear superposition of the two.

[0027] Step B: Establish the analysis and prediction formula for the local scour expansion rate of underwater structures

[0028] By conducting physical experiments on the apparent scouring rate of soil, a prediction formula for the apparent scouring rate of soil was established as shown in formula (5). The form of this formula is relatively simple, but it can physically reflect the nature of local scouring, that is, the fundamental reason for the scouring of any soil is that the seabed shear stress caused by fluid conditions (unidirectional flow, waves, and the combined action of waves and currents, etc.) is greater than the critical shear stress of the soil. However, it should be noted that in the physical experiment on the apparent scouring rate of soil, there is no structure, and only the scouring characteristics of the soil are studied. When there is a structure, the structure will narrow the water-passing section, thereby causing the fluid flow around the structure to accelerate the flow rate, resulting in a stress amplification effect on the seabed around the structure. Therefore, when there is a structure, the nature of scouring has not changed, but it is necessary to consider the stress amplification effect of local scouring caused by the existence of the structure. Therefore, formula (5) is still valid for local scouring caused by the presence of structures. Based on this principle, an accurate prediction formula for the local scouring extension rate of submarine structures is established:

[0029]

[0030] Where ψ(t) represents the local scour expansion rate around the structure. Different from the apparent scour rate of the soil, χ, ψ(t) represents the local scour caused by the amplification of the local seabed stress due to the existence of the structure. α represents the shear stress amplification factor of the local seabed around the structure, which is defined as α = τ / τ ∞ , where τ represents the seabed shear stress around the structure; τ ∞represents the seabed shear stress at infinity without being disturbed by the structure. This shear stress is calculated by formulas (6) and (7) under unidirectional flow conditions. For the flow conditions of waves and wave-current combined action, the seabed shear stress at infinity is calculated by formulas (6) and (7). It can be seen from formula (8) that the key to predicting the local scour expansion rate of underwater structures is to obtain the seabed shear stress τ around the structure, which is difficult to obtain by analyzing the velocity profile. The fundamental reason is that due to the obstruction of the structure, the distribution of the velocity around the structure along the depth direction no longer conforms to the logarithmic rate distribution form shown in formula (6). The seabed shear stress τ around the structure can be obtained by two methods: 1) Conducting physical experiments, measuring the flow field information around the structure, and obtaining the seabed shear stress τ by calculating the spatial gradient of the velocity profile; however, the existing velocity measurement equipment is basically invasive and requires a certain depth of water to measure the velocity, which will inevitably cause serious disturbances to the flow field around the structure, and the relevant measurement data will have large errors; 2) Obtaining the seabed shear stress τ around the structure through numerical simulation; Compared with physical experiments, numerical simulation can obtain complete flow field information, and then obtain the distribution of seabed shear stress in time and space. Limited by the measurement equipment, this is almost impossible to achieve in physical experiments. In addition, another advantage of numerical simulation is that in order to obtain the seabed shear stress around the structure, there is no need to carry out local scouring calculations. The fundamental reason is that the shear stress of the seabed is controlled by the form of the structure and the flow conditions, and has a weak dependence on the type of sediment, which will greatly save calculation time. Through the method of numerical simulation, the local scouring problem of underwater structures can be transformed into a traditional hydrodynamic problem of marine engineering, so the problem of local scouring scale effect can be effectively overcome.

[0031] The numerical simulation of the hydrodynamics of underwater structures is often a turbulent flow problem, which requires the introduction of a model for turbulent closure. Due to the obvious adverse pressure gradient around the structure, the SST k-ω two-equation turbulence model is used to improve the accuracy of numerical simulation. Different seabed sediments will cause different roughness heights of the seabed, which in turn affects the flow structure around the structure. In order to obtain accurate seabed shear stress, the turbulent kinetic energy generation term ω in the turbulence model introduces the following boundary conditions to simulate the seabed roughness caused by different sediments:

[0032]

[0033] Among them, ν represents the viscosity coefficient of the fluid, and the system S r The calculation expression is:

[0034]

[0035] In the above formula, k s+ =2.5d 50 u* / ν; From formula (10), it can be seen that this boundary condition mainly depends on the median particle size d of the sediment. 50 , and has nothing to do with the characteristics of the sediment. For detailed information on the turbulence model and the above boundary conditions, please refer to the previous work carried out by the applicant of the present invention (Tang GQ, Cheng L., Lu L., Teng YF, Zhao M., An HW, 2018. Effect of oscillatory boundary layer on hydrodynamic forces on pipelines. Coast. Eng., 140: 114–123.).

[0036] After the local scour expansion rate around the structure is obtained by formula (8), the change of the local scour depth around the structure over time is calculated by the following formula:

[0037]

[0038] It can be seen from the above formula that the development process of local scour around the structure over time can be obtained through formula (11); in addition, this formula can also consider the influence of changes in flow velocity and flow direction over time on local scour. Its core is to consider the changes in seabed shear stress caused by changes in flow velocity and flow direction. These cannot be considered in traditional analysis and prediction models, which is also the obvious advantage of this method.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. This method can accurately predict the local scouring characteristics of underwater structures and can effectively overcome the scale effect problem of local scouring physical experiments of sediment.

[0041] 2. The local scour problem of underwater structure sediment is transformed into a traditional marine engineering hydrodynamic problem. At the same time, the new method proposed by the present invention can take into account the change of flow conditions over time and the change of flow direction, which cannot be considered in the previous local scour analysis and prediction model. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Diagram showing the setup of a physical experiment on apparent scour rate of soil.

[0043] Figure 2 is the relationship between the apparent scouring rate χ of the soil and the seabed shear stress τ.

[0044] Figure 3 Diagram showing the setup for the local scour physics experiment on an underwater vertical cylinder.

[0045] Figure 4 The variation of the local scour depth S / D of a vertical cylinder with time t obtained by experimental measurement, where the Reynolds number Re=51700.

[0046] Figure 5 Comparison between the local scour expansion rate ψ of the underwater vertical cylinder predicted by formula (8) and the monitoring results of physical experiments.

[0047] In the figure: 1-acoustic Doppler current meter; 2-3D sonar probe; 3-soil sample flushing box; 4-vertical cylinder; 5-contact image sensor; 6-rectifier. DETAILED DESCRIPTION

[0048] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0049] like Figure 1 As shown, the physical experiment carried out using the method of the present invention is as follows:

[0050] The physical experiment on the apparent scour rate of soil involved in the present invention was carried out in the PIV flume of the State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology. The flume is 23m long, 0.8m wide and 0.8m deep. The relevant physical test section steps are in the middle part of the flume. A soil sample scour box 3 with a length of 20cm, a width of 10cm and a depth of 6cm was arranged in the test section to carry out the physical experiment on the apparent scour rate of soil. Slopes made of concrete with a ratio of 1:10 were set on both sides of the test section to ensure that the incoming flow can smoothly transition to the test section. The test water depth was 0.3m, and a total of 2 types of loose and uniform sand were used, with a median particle size d 50 =0.17mm and 0.38mm. The corresponding flow condition is unidirectional flow. By setting the flow velocities of multiple unidirectional flows, the relationship between the apparent scouring rate of the soil and the seabed shear stress is analyzed. In the experiment, the velocity profile is measured by an acoustic Doppler velocimeter 1 (ADV), and the seabed shear stress τ is calculated by formulas (6) and (7): c For each unidirectional flow velocity, the test was carried out for 3 minutes, and the scouring depth of the sand sample was detected in real time through the 3D sonar probe 2. After the 3-minute physical test, the average sand bed change height was calculated and divided by time to obtain the apparent scouring rate of the soil, χ, combined with the obtained seabed shear stress τ c , a quantitative relationship between the two can be established. The relevant physical test results are as follows Figure 2 As shown (in d 50 =0.17 mm as an example). In addition, Table 1 gives the dimensionless critical shear stress τ of different loose uniform sands obtained through experimental measurements. cr *Comparison of critical shear stress obtained with the prediction of existing empirical formulas (Formulas 12-14).

[0051] τ cr =θ cr ρg(s-1)d 50 (12)

[0052]

[0053]

[0054] Table 1 Comparison of the dimensionless critical starting stress of loose sand obtained experimentally and the empirical prediction formula

[0055]

[0056] Among them, s represents the ratio of the density of the test sand to the density of the water body, θ cr represents the critical Shields parameter of the sediment, and g represents the acceleration of gravity. From the comparison results in Table 1, it can be seen that the critical shear stress of the sand sample obtained by the test analysis of the present invention is in good agreement with the result obtained by the empirical prediction formula, which proves the accuracy of the test method. However, it should be noted that formulas (12)-(14) are only applicable to loose and uniform sand, and for sediments with viscous effects commonly seen at engineering sites, the difference in the prediction accuracy of the critical starting stress of sediments between these two formulas is often several times lower than the actual critical starting stress of seabed sediments. This is also the fundamental reason why physical tests on the apparent scour rate of soil must be carried out for soil at engineering sites.

[0057] In order to verify the effectiveness of the method proposed in this paper, a physical experiment of local scouring of underwater vertical piles was carried out in the O-Tube experimental device of the State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology. The relevant experimental settings are as follows: Figure 3 As shown. The dimensions of the O-Tube experimental device are 28.2m long, 1.5m wide and 1.6m deep. The middle of the water tank is the experimental section, which is 18.0m long. Both ends are provided with honeycomb-shaped flow stabilization devices, i.e., rectifiers 6, which are 5.1m long. There is a sunken section in the middle of the experimental section, which is 8.0m long, in which the median particle size d 50 = 0.17mm loose uniform sand, with a maximum thickness of 40cm. The water depth of the experiment is 1m. The velocity profile in the experiment is measured by an acoustic Doppler current meter 1, and the average velocity of the cross section is U = 0.41m / s. The vertical cylinder 4 is located in the middle of the water tank, with a total of 6 groups of diameters D = 35mm, 50cm, 75mm, 100mm, 125mm, and 150mm, and the corresponding Reynolds number Re = UD / ν = 2.06×10 5 ~6.2×10 5; A contact image sensor 5 is arranged on the side surface of the vertical cylinder 4. The change of the relevant flushing depth over time is as follows Figure 4 As shown (Re = 5.17 × 10 5 ).from Figure 4 It can be seen from the figure that in the initial results of scouring, the scouring depth changes dramatically with time. As time goes by, the scouring depth changes slowly and eventually tends to balance. Formula (8) mainly predicts the expansion rate of local scouring. In order to verify the effectiveness of the method proposed in this invention, it is compared with the results of the physical experiment. In the experiment, the slope of the curve in the faster scouring development stage is taken as the scouring expansion rate. The relevant comparison results are as follows: Figure 5 As shown, it should be noted that when using formula (8) to predict the scour expansion rate of the vertical cylinder 4 facing the flow to the front under the action of unidirectional flow, the seabed stress amplification coefficient of the vertical cylinder facing the flow to the front in formula (8) is obtained through the work carried out by predecessors (Roulund et al., Journal of Fluid Mechanics, 2005, 534: 351-401). Figure 5 From the comparison results, it can be seen that the results obtained by analyzing the prediction method of the local scour expansion rate proposed in the present invention are well compared with the results of the physical experiment, which verifies the accuracy of the method proposed in the present invention. Since this method is based on the transport characteristics of the soil, there is no model scale effect problem that is common in sediment scour physical experiments. Therefore, it can well overcome the scale effect problem of sediment physical experiments and has a strong engineering application value. In addition, the core of this method is to obtain the stress method coefficient of the seabed around the structure. This coefficient can be obtained through traditional marine engineering hydrodynamic methods. Therefore, the local scour problem of the structure can be converted into a hydrodynamic coefficient problem of the structure, which is also the advantage of this method.

Claims

1. A method for overcoming the scale effect problem in a physical experiment of local scouring of underwater structures, characterized in that: The following steps are involved: Step A: Establishing different sediment transport characteristics formulas Physical experiments on the apparent scour rate of soil were carried out to obtain the quantitative relationship between the apparent scour rate of soil and the shear stress of the seabed under different flow conditions, as well as the critical starting stress. By carrying out physical experiments on the apparent scour rate of soil under different flow conditions, a prediction formula for the apparent scour rate of soil was established: x=s(t c -t cr ) ε (1) Among them, χ represents the apparent scour rate of soil, which represents the scour depth of soil without structure under certain flow conditions per unit time; σ and ε are constant coefficients, which are obtained by fitting the data obtained from the physical experiment of apparent scour of soil by the least square method. The two constant coefficients represent the transport capacity of soil; τ cr Represents the critical shear stress of the soil, which characterizes the soil's ability to resist scour; τ c represents the seabed shear stress caused by fluid flow; when τ c >τ cr When the soil is transported, scouring occurs; the seabed shear stress is obtained by analyzing the velocity profile obtained by measurement. Under the action of the fluid, the distribution of the horizontal velocity in the depth direction conforms to the following logarithmic rate distribution: Where U(z) represents the horizontal velocity measured at height z, κ = 0.4 represents the Karman constant coefficient, z0 represents the seabed roughness height, and the median particle size d of the seabed sediment is 50 The calculation method is z0=d 50 / 12,u * Represents the bottom friction velocity. When the velocity at a point in space is known, use formula (2) to calculate the bottom friction velocity. When the sea condition is a unidirectional flow, the seabed shear stress τ in formula (1) is c The following formula is used for calculation: Among them, ρ represents the density of water; The critical shear stress of soil in formula (1) is calculated as follows: when the apparent scour rate of soil is χ = 10 -7 m / s corresponding to the seabed shear stress. This method for analyzing the critical shear stress of soil is also applicable to the flow conditions of wave and wave-current combined action; When the sea condition is wave-like, it is necessary to select the velocity profile when the boundary layer is fully developed, and then calculate the seabed shear stress τ caused by the wave condition using formulas (2) and (3): c ; When the sea condition is a combined effect of waves and currents, the seabed shear stress is obtained by analyzing the linear superposition of the seabed shear stress caused by unidirectional flow and the seabed shear stress caused by wave conditions; Step B: Establish the analysis and prediction formula for the local scour expansion rate of underwater structures Establish an accurate prediction formula for the local scour expansion rate of submarine structures: Where ψ(t) represents the local scour expansion rate around the structure. Different from the apparent scour rate of the soil, χ, ψ(t) represents the local scour caused by the amplification of the local seabed stress due to the existence of the structure. α represents the shear stress amplification factor of the local seabed around the structure, which is defined as α = τ / τ ∞ , where τ represents the seabed shear stress around the structure; τ ∞ represents the seabed shear stress at infinity without being disturbed by the structure. The shear stress is calculated by formulas (2) and (3) under unidirectional flow conditions. For wave and wave-current combined flow conditions, the seabed shear stress at infinity is calculated by formulas (2) and (3). The seabed shear stress τ around the structure is obtained by two methods: 1) conducting physical experiments, measuring the flow field information around the structure, and obtaining the seabed shear stress τ by calculating the spatial gradient of the velocity profile; 2) obtaining the seabed shear stress τ around the structure by numerical simulation. For the numerical simulation of the hydrodynamics of underwater structures, a model is introduced for turbulent closure. Due to the obvious adverse pressure gradient around the structure, the SST k-ω two-equation turbulence model is used to improve the accuracy of numerical simulation. In order to obtain accurate seabed shear stress, the turbulent kinetic energy generation term ω in the turbulence model introduces the following boundary conditions to simulate the seabed roughness caused by different sediments: Where ν represents the viscosity coefficient of the fluid, and the system S r The calculation expression is: In the above formula, k s + =2.5d 50 u * / ν; After the local scour expansion rate around the structure is obtained by formula (4), the change of the local scour depth around the structure over time is calculated by the following formula:

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