Method for evaluating transport rate of sediment under action of waves and of combination of waves and currents

Abstract

The present invention relates to the field of seabed sediment scour research, and discloses a method for evaluating the transport rate of sediment under the action of waves and of combination of waves and currents. The local scour of a seabed structure is closely related to the transport rate and critical shear stress of sediment. At present, the prediction of the transport rate and critical shear stress of sediment is performed for loose uniform sediment, while there is a large error in the related prediction of viscous sediment. In the present invention, on the basis of physical experiments on apparent sediment scour rates, a parameter description method for the transport rate and critical starting stress of any type of sediment under complex wave and wave-current combination conditions is provided, thereby overcoming the defect that existing empirical formulas can only be used for loose uniform sediment. The method provided by the present invention allows for accurate prediction of the transport rate and critical shear stress of any type of sediment under the wave and wave-current combination conditions, and can provide a scientific basis and technical guarantee for the evaluation of the local scour and safety design of the seabed structure.

Description

A method for evaluating soil transport rate under combined wave and wave-current conditions. Technical Field

[0001] This invention belongs to the field of research on seabed sediment scour and relates to a method for evaluating soil transport rate under the combined action of waves and wave currents. Background Technology

[0002] Submarine cables typically have long routes, ranging from tens to hundreds of kilometers. Their routes may involve diverse seabed sediment conditions, such as silt, fine sand, medium and medium-coarse sand, mud, silty clay, and silty loam. These soil types exhibit significantly different critical initiation conditions and transport patterns (suspended sediment transport alone, bedload transport alone, and both suspended and bedload transport), resulting in substantial differences in the local scour characteristics around the cable. Furthermore, seabed soil often exhibits stratification along its depth, posing significant technical challenges to the engineering prediction of localized scour of the cable and the dynamic evolution of seabed geomorphology, including sand waves and ridges. Research conducted by the project team has shown that for sediments with weak interparticle cohesion, such as silt, fine sand, and medium sand, the critical initiation stress can be analyzed using the empirical formula established by Soulsby (Dynamics of marine sands: a manual for practical applications, 1997, Thomas Telford), with good accuracy. However, for soils with significant cohesion, such as silt, silty clay, and silty loam, the empirical formula established by Soulsby (1997) often gives an excessively low estimate of the critical initiation stress, leading to a large error between the predicted results and the actual values. Currently, there is no mature theoretical formula for predicting the critical initiation stress of cohesive soils.

[0003] Local scour of any type of subsea structure is closely related to the critical initiation stress and transport rate of the soil. Currently, for cohesive loose sand, researchers have established relatively complete methods for assessing its transport rate and critical initiation stress. However, research on soils with significant cohesive effects, commonly found in engineering, remains significantly lacking. Mohr et al. (Mohr H., Draper S., Cheng L., White DJ Predicting the rate of scour beneath subsea pipelines in marine sediments under steady flow conditions, Coastal Engineering, 2016, 110: 111-126.) pioneered a physical experimental method for the apparent scour rate of soil. This experiment only considers unidirectional flow conditions. In the experiment, by applying different unidirectional flow velocities to the soil sample, the soil's expansion rate in the depth direction was measured, ultimately establishing a functional relationship between the soil transport rate η and the seabed shear stress τ caused by the flow, i.e., η = M(τ - τ). cr ) n Where M and n are constant coefficients, τ cr The critical shear stress of the soil is represented by these parameters, which can be obtained by fitting experimental data using the least squares method. For localized scour of submarine structures, the physical meaning of this formula is that localized scour occurs when the shear stress of the seabed surrounding the structure exceeds the critical shear stress of the soil. Therefore, once the soil transport rate is obtained, theoretically, the development process and equilibrium profile of localized scour of any structural form can be accurately predicted.

[0004] It should be noted that the research by Mohr et al. (2016) focused on unidirectional flow. Under unidirectional flow conditions, the resulting seabed shear stress is independent of time. However, for more complex wave and wave-current combined conditions, the resulting seabed shear gravity is closely related to time. Therefore, the soil transport rate formula established by Mohr et al. (2016) under unidirectional flow conditions is not applicable. Therefore, this invention will develop a method for evaluating soil transport rate under the combined action of waves and wave-currents. This method further enriches and develops the theory of sediment transport mechanics, and also makes the accurate prediction of the local scour characteristics of seabed structures under more complex flow conditions theoretically possible. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies and to provide an accurate assessment method for the transport rate of cohesive soil under complex flow conditions, the present invention aims to provide a method applicable to assessing soil transport rate under combined wave and wave-current conditions. This overcomes the limitations of existing research, which can only consider soil transport rate under unidirectional flow conditions and cannot account for the transport rate of cohesive soil under more complex combined wave and wave-current conditions. Thus, it provides a scientific basis and technical guarantee for the assessment of local scour and safety design of submarine structures.

[0006] The technical solution of this invention:

[0007] A method for evaluating soil transport rate under combined wave and wave-current conditions includes the following steps:

[0008] (1) Determination of critical shear stress in soil

[0009] For underwater structures, the types of seabed soil they encounter are diverse. For loose, non-cohesive sand, the critical shear stress can be predicted using the empirical formula established by Soulsby (1997). However, for soil types with significant cohesive effects, Soulsby's (1997) empirical formula provides an underestimation, leading to significant errors in the assessment of local scour of the structure. For cohesive soils, no reliable theoretical or empirical prediction formula has yet been established, making it impossible to quickly predict the critical shear stress of cohesive soils.

[0010] Theoretically, the critical shear stress of soil is an inherent property, independent of flow conditions. Therefore, physical experiments on the apparent scour rate of soil under unidirectional flow conditions can be conducted to establish the following quantitative relationship between soil transport rate and seabed shear stress and critical shear stress:

[0011] (1)

[0012] Where η represents the soil transport rate, which physically represents the depth of soil scour per unit time; τ represents the seabed shear stress caused by flow. For unidirectional flow, it can be predicted using a logarithmic rate formula. M and n represent constant coefficients reflecting the soil's transport capacity, and τ... cr The critical shear stress of the soil can be obtained by fitting the experimental data using the least squares method. To ensure fitting accuracy, at least six sets of unidirectional flow velocities should be used when conducting physical experiments on the apparent scour rate of soil under unidirectional flow.

[0013] (2) Determination of seabed shear stress caused by different flow conditions

[0014] As can be seen from formula (1), the core of the soil transport rate formula is to determine the seabed shear stress caused by different flow conditions. For unidirectional flow, the distribution of horizontal velocity along the water depth satisfies the following logarithmic law formula:

[0015] (2)

[0016] Where u(z) represents the horizontal flow velocity at a water depth of z; The value represents the bottom friction velocity; κ = 0.4 represents the Karman constant coefficient; z s This represents the seabed roughness length, which, for sandy seabeds, is taken as d. 50 / 12,d 50 This represents the median particle size of the sediment. From formula (2), it can be seen that for unidirectional flow, the seabed shear stress τ is independent of time. When the horizontal velocity u(z) at spatial location z is measured, the bottom friction velocity u can be calculated. The formula for calculating the seabed shear stress caused by this flow velocity is τ=ρu 2 .

[0017] Unlike unidirectional currents, wave-current and wave-current combined conditions exhibit distinct periodicity in water particle movement, leading to a significant periodicity in the corresponding seabed shear stress. Therefore, formula (1) cannot be directly used to assess sediment transport rates under wave-current combined conditions. Currently, the periodic average of the absolute value of instantaneous seabed shear stress is typically used to represent the characteristic seabed shear stress τ in calculations related to sediment transport under wave conditions. w (Zou Zhili, Coastal Dynamics, 4th Edition, 2009, People's Communications Press), and further used for the calculation and analysis of sediment transport. Therefore, the characteristic seabed shear stress τ w Accurate calculation requires first clarifying the periodic variation characteristics of seabed shear stress under wave conditions. The spatiotemporal distribution of seabed shear stress under wave action can be calculated using the following formula:

[0018] (3)

[0019] Where ω represents the wave's angular frequency. The amplitude of the velocity of wave particles outside the boundary layer is represented by ρ, where ρ represents the density of the water body, and i is a unit imaginary number. This represents the shear stress on the seabed. λ1, λ2, p1, and p2 are characteristic parameters, and their calculation formulas are as follows:

[0020] (4)

[0021] (5)

[0022] (6)

[0023] (7)

[0024] Where, k s This represents the seabed roughness height, for sandy seabeds k s = 2.5d 50 d 50 Let represent the roughness height of the seabed, and 'a' represent the displacement amplitude of wave-induced water particle motion outside the boundary layer. Using the above formula, the spatiotemporal distribution of seabed shear stress under wave conditions can be obtained, and thus the characteristic seabed shear stress τ can be derived. w .

[0025] For sediment transport under the combined action of waves and currents, the characteristic seabed shear stress τ wc The following formula can be used for calculation (Zou Zhili, Coastal Dynamics, 4th Edition, 2009, People's Communications Press):

[0026] (8)

[0027] Where, τ c This represents the seabed shear force caused by unidirectional current. The characteristic seabed shear stress τ under wave conditions is obtained. w and the characteristic seabed shear stress τ under the combined action of waves and currents wc Substituting into formula (1), we can achieve an accurate prediction of the soil transport rate under the combined action of waves and wave currents.

[0028] The beneficial effects of this invention are:

[0029] The method established by this invention enables the assessment of transport rate and critical initiation stress in cohesive soils under complex wave and wave-current combined conditions. This overcomes the major limitation of existing empirical formulas, which are mainly applicable to loose, non-cohesive sand and cannot accurately predict the transport rate of soils with significant cohesive effects. The method established by this invention can provide a scientific basis and technical guarantee for the assessment and safety design of local scour of seabed structures. Attached Figure Description

[0030] Figure 1 is a schematic diagram of the physical experimental setup for the apparent scour rate of soil.

[0031] Figure 2 shows the quantitative relationship between soil scour rate and seabed shear stress.

[0032] Figure 3 shows a comparison between the critical shear stress of loose sand measured experimentally and the empirical formula.

[0033] Figure 4 shows a comparison between the critical shear stress of cohesive soil measured experimentally and the empirical formula.

[0034] Figure 5 shows a comparison between the spatiotemporal distribution of seabed shear stress calculated by the formula and the experimental results of others; Detailed Implementation

[0035] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0036] First, a physical experiment on the apparent scour rate under unidirectional flow conditions was conducted to establish a quantitative relationship between soil transport rate and seabed shear stress and critical shear stress. The relevant physical experiment setup is shown in Figure 1. 1 represents the physical experiment terrain, which can be formed by pouring concrete. To ensure a smooth transition of the incoming flow to the experimental section, 1:10 slopes 2 were arranged at both ends of the experimental terrain. 3 represents a soil sample box, used to arrange the test soil. During the experiment, the surface of the soil needs to be flat and flush with the surrounding terrain. The length of the soil sample box is 20cm, and the depth and width are both 10cm. A laser Doppler current meter 4 is arranged 5cm above the soil sample box 3 to measure the incoming flow velocity, and then the shear stress caused by the incoming flow is calculated using formula (2). 5 represents a three-dimensional laser terrain scanner, used to measure the elevation change of the soil. Assuming the scour depth is s within time t, the scour rate of the soil is η = s / t.

[0037] Figure 2 shows the results obtained from the physical experiment on the apparent scour rate of the soil. The black dots represent the results measured by the physical experiment, and the black lines represent the results obtained by fitting using the least squares method. The relevant results can be expressed using formula (1), and then the critical seabed shear stress τ can be obtained. cr Through physical experimental analysis, the formula for the apparent erosion rate of soil is obtained as η = 1.697 × 10⁻⁶. -4 (τ-0.189) 1.263 That is, the critical seabed shear stress is 0.189 Pa.

[0038] Figure 3 shows a comparison between the critical shear stress of loose sand obtained from physical experiments and the empirical formula established by Soulsby (1997). The dots represent the experimental measurements, and the black line represents the predicted result from Soulsby's (1997) empirical formula. As can be seen from the figure, for loose sand, the results obtained from physical experiments are consistent with the predicted results from the empirical formula, verifying the reliability of the relevant physical experimental methods.

[0039] Figure 4 shows a comparison between the critical shear stress of cohesive soil obtained from physical experiments and the empirical formula established by Soulsby (1997). The dots represent experimental measurements, and the black line represents the prediction result from Soulsby's (1997) empirical formula. As can be seen from the figure, the critical initiation stress of cohesive soil is significantly higher than that of loose sand under the same median grain size conditions. Therefore, using the empirical formula established by Soulsby (1997) to predict the critical initiation stress of cohesive soil will give a lower estimate.

[0040] Figure 5 shows a comparison between the spatiotemporal distribution of seabed shear stress predicted using formulas (3) to (7) and the results of physical experiments by Jensen et al. (1989). As can be seen from the figure, the results predicted by the formulas show good agreement with the physical experimental results, verifying the effectiveness of the method proposed in this invention. Using formulas (3) to (7), the spatiotemporal distribution of seabed shear stress under wave conditions can be predicted, thereby obtaining the characteristic seabed shear stress τ. w Substituting this into formula (1) and combining it with formula (8), we can achieve an accurate prediction of the soil transport rate under the combined action of waves and wave currents.

Claims

1. A method for evaluating soil transport rate under combined wave and wave-current conditions, characterized in that, Includes the following steps: (1) Determination of critical shear stress in soil Physical experiments were conducted on the apparent scour rate of soil under unidirectional flow conditions to establish the following quantitative relationship between soil transport rate and seabed shear stress and critical shear stress: (1) Where η represents the soil transport rate, its physical meaning being the depth of soil scour per unit time; τ represents the seabed shear stress caused by flow; for unidirectional flow, it can be predicted using a logarithmic rate formula; M and n represent constant coefficients reflecting the soil's transport capacity, τ cr The critical shear stress of the soil can be obtained by fitting the experimental data using the least squares method. (2) Determination of seabed shear stress caused by different flow conditions As can be seen from formula (1), the core of the soil transport rate formula is to determine the seabed shear stress caused by different flow conditions; for unidirectional flow, the distribution of horizontal velocity along the water depth satisfies the following logarithmic law formula: (2) Where u(z) represents the horizontal flow velocity at a water depth of z; The value represents the bottom friction velocity; κ=0.4 represents the Karman constant coefficient; z s This represents the seabed roughness length, which, for sandy seabeds, is taken as d. 50 / 12,d 50 Indicates the median particle size of sediment; It can be seen from formula (2) that for unidirectional flow, the seabed shear stress τ is independent of time. When the horizontal velocity u(z) at spatial point z is measured, the bottom friction velocity u can be calculated. The formula for calculating the seabed shear stress caused by this flow velocity is τ=ρu 2 Where ρ represents the density of water; Unlike unidirectional currents, wave-current and wave-current combined conditions exhibit distinct periodicity in water particle movement, leading to a corresponding periodicity in seabed shear stress. Therefore, formula (1) cannot be directly used to assess sediment transport rate under wave-current combined conditions; characteristic seabed shear stress τ w Accurate calculation requires first clarifying the periodic variation characteristics of seabed shear stress under wave conditions; the spatiotemporal distribution of seabed shear stress under wave action can be calculated using the following formula: (3) Where ω represents the wave's angular frequency. The amplitude of the velocity of wave particles outside the boundary layer is represented by ρ, where ρ represents the density of the water body, and i is a unit imaginary number. The shear stress on the seabed is represented by λ1, λ2, p1, and p2; these are characteristic parameters, and their calculation formulas are as follows: (4) (5) (6) (7) Where, k s This represents the seabed roughness height, for sandy seabeds k s =2.5d 50 d 50 Let represent the roughness height of the seabed, and 'a' represent the displacement amplitude of wave-induced water particle motion outside the boundary layer. Using the above formula, the spatiotemporal distribution of seabed shear stress under wave conditions can be obtained, and thus the characteristic seabed shear stress τ can be derived. w ; For sediment transport under the combined action of waves and currents, the characteristic seabed shear stress τ wc The following formula can be used for calculation: (8) Where, τ c This represents the seabed shear force caused by unidirectional flow; by obtaining the characteristic seabed shear stress τ under wave conditions. w and the characteristic seabed shear stress τ under the combined action of waves and currents wc Substituting into formula (1), we can achieve an accurate prediction of the soil transport rate under the combined action of waves and wave currents.

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