A comprehensive risk assessment method for scour and seepage of dikes at different times during ice flood season

Abstract

The present invention discloses a method for evaluating the comprehensive risk of dike scouring and seepage at different periods during the ice flood period. The ice flood period is divided into three periods: ice flow period, river closure period and river opening period according to the evolution process of river ice conditions; the characteristics of ice-water conditions and dike conditions at different periods during the ice flood period are analyzed, and different characteristic indicators at different periods during the ice flood period are compared and analyzed to identify the influence mechanism of ice / water / sand external conditions coupling driving on the evolution of the comprehensive risk of dike scouring and seepage; the dike scouring risk at different periods during the ice flood period is quantified; the dike seepage risk at different periods during the ice flood period is quantified, and the evaluation matrix of the comprehensive risk of dike scouring and seepage at different periods during the ice flood period is constructed by using the fused dike scouring risk and dike seepage risk to evaluate the comprehensive risk of dike scouring and seepage at different periods during the ice flood period. The present invention provides a scientific basis for the risk management of dike engineering disasters during the ice flood period and the formulation of ice prevention and disaster reduction measures, and improves the theoretical and technical level of dike disaster defense during the ice flood period.

Description

Technical Field

[0001] The present invention relates to the field of risk assessment technology in the field of emergency disaster prevention and water conservancy informationization, and in particular to a method for assessing the comprehensive risk of levees at different periods during an ice flood season. Background Art

[0002] The risk assessment of levees during the ice flood season is an important technical means to conduct a comprehensive analysis and quantitative evaluation of the risks faced by levees during the ice flood season. It is also one of the important non-engineering measures to fully understand the comprehensive safety status of levees in different periods of time and disaster risk management.

[0003] Compared with the summer and autumn flood season, the ice flood season is affected by multiple factors such as the rapid rise and fall of river water levels, frozen soil, and ice, and the scouring and seepage risks faced by embankment projects have increased significantly. Although there are a large number of research results on risk assessment of embankment projects, there are still significant deficiencies. On the one hand, current research often focuses on the analysis and assessment of a single risk (such as scouring or seepage), while the rise and fall of river water levels will cause embankment scouring and seepage risks at the same time. There is still a lack of comprehensive assessment methods for scouring and seepage risks that consider the interaction of multiple factors. During the ice flood season, the scouring risk and seepage risk of dikes change with the evolution of the ice-water conditions in the river channel and the dike conditions. In addition, for dike projects, the scouring and seepage risks occur almost simultaneously. Considering a single risk factor does not fully match the actual disaster situation. On the other hand, most of the simulation and assessment of ice flood risks are based on a fixed river channel in a specific period, using one- and two-dimensional ice-water dynamics methods. The temporal and spatial variation patterns of the comprehensive risk of dikes under the influence of multiple characteristic indicators of ice, water, sand and temperature at different periods of the ice flood season, different typical dangerous sections of dikes, and ice, water, sand and temperature have not been explored, making it difficult to provide practical and effective scientific guidance for disaster prevention of dike projects during the ice flood season.

[0004] The scour risk and seepage risk faced by levees during the ice flood season are both core elements in the levee risk assessment system. Relying on any one risk alone as the evaluation benchmark for the overall safety of the levee can provide insight into the potential dangers of the levee to a certain extent, but due to the limitations of its consideration dimensions, it is difficult to fully and accurately cover the complexity and variability of levee risk assessment, which may affect the integrity and accuracy of the assessment results.

[0005] In summary, the comprehensive risk of scouring and seepage of dikes during the ice flood period changes with the changes of external influencing factors, that is, the comprehensive risk corresponding to different periods is different and changes over time. However, the current assessment method for the risk of dikes during the ice flood period is limited to the consideration of single factors such as scouring and seepage, and it is difficult to comprehensively and accurately quantify the degree of dike danger at different periods during the ice flood period. Summary of the invention

[0006] In view of the practical problem that the existing levee risk assessment methods are difficult to meet the comprehensive risk assessment of scour and seepage in key dangerous sections of levees under the changing environment of ice flood season, the present invention aims to propose a comprehensive risk assessment method for scour and seepage in levees at different periods of ice flood season, taking into account the characteristic indicators of ice water, sand temperature at different periods of ice flood season and their impact on scour and seepage risks of levees, and establishing a mathematical model to improve the comprehensiveness and accuracy of scour and seepage risk assessment of levees, so as to obtain the comprehensive risk assessment results of scour and seepage in key dangerous sections of levees.

[0007] The present invention proposes a comprehensive risk assessment method for dike scour-seepage during ice flood season, comprising:

[0008] S1. According to the evolution of river ice conditions, the ice flood season is divided into three periods: floating ice period, river closure period and river opening period;

[0009] S2. Analyze the characteristics of ice-water conditions and embankment conditions at different times during the ice flood season, at least determine the characteristics of river ice conditions, water conditions, sediment transport, embankment seepage and frozen soil in each stage, explore the temporal and spatial variation laws and differentiation characteristics of the same characteristic indicators in different time periods, and explore the driving correlation mechanism between the characteristic indicators at different times during the ice flood season. Through comparative analysis of different characteristic indicators at different times during the ice flood season, identify the impact mechanism of the coupling drive of ice / water / sand external conditions on the evolution of the comprehensive risk of embankment scour-seepage;

[0010] S3. Quantify the risk of dike scour at different times during the ice flood season;

[0011] S4. Quantify the seepage risk of dikes at different times during the ice flood season;

[0012] S5. Using the integrated embankment scour risk and embankment seepage risk, the embankment scour-seepage comprehensive risk at different times during the ice flood season is evaluated: the subjective weight vector W is used. 1 and the objective weight vector W 2 The subjective and objective combined weighting method is used to optimize the weighting, and the risk weights of the embankment scour risk and seepage risk in each period are allocated to the comprehensive risk degree. The characteristic coupling of different periods and different risks is realized to calculate the comprehensive risk degree in different periods; the scour, seepage and comprehensive hazard characteristics of different periods are compared and analyzed to evaluate the comprehensive risk degree of embankment scour and seepage in different periods during the ice flood season.

[0013] In some embodiments, S1 further includes: ice condition characteristic indicators at least include ice body morphology, drift ice, ice cover, ice thickness, ice jams and ice dams; water condition characteristic indicators at least include changes in water level, flow rate and flow velocity; sediment transport at least includes sediment content and sediment transport rate; ice-water dynamics characteristic indicators at least include the movement law of ice in the river, the interaction between ice and water flow and the impact on the river; embankment engineering condition characteristic indicators at least include embankment seepage and embankment freezing conditions; through comparative analysis of different ice flood periods and different characteristic indicators, the influence mechanism of the coupling drive of external conditions such as ice / water / sand on the evolution of the comprehensive risk of embankment scour-seepage is identified.

[0014] In some embodiments, the dike scour risk at different time periods in S3 is calculated based on the boundary conditions of the dike scour simulation at different time periods during the ice flood season, and a two-dimensional mathematical coupling model of river channel and dike ice, water and sand is run to obtain the dike scour hazard index, and the slope toe lateral erosion distance in the dike scour hazard index is used as the dike scour risk.

[0015] In some embodiments, the calculation formula for dike scour risk at different time periods is as follows:

[0016]

[0017] The calculation formula of dike scour risk during the whole period (from ice flow period to the end of river opening period) is as follows: CS = t (CS 1 ,CS 2 ,CS 3 )

[0018] Among them, f 1 、f 2 、f 3 Solve the process function for the numerical model at different time periods, y 1 ,y 2 ,y 3 To compare the difference function of the side erosion distance ΔB of the slope foot in different dangerous sections of the embankment during the same period, ΔB 1 , ΔB 2 , ΔB 3 The side erosion distance of the slope foot at different periods, C l is the lateral scour coefficient, τ is the shear stress of nearshore flow, τ c is the anti-impact force of the slope soil, γ is the bulk density of the slope soil, Δt is the flood erosion time, h is the total water head, is the average value of the velocity components in the x and y directions based on the water depth, T ij is the lateral stress term T xx , T xy , T yy Any item in, S is the point source flow, ω * is the sediment settling velocity, S b1is the bed load transport rate, S XY is the suspended sediment holding force, is the velocity of the flow under the ice sheet or ice sheet surface, c f is the drag coefficient, M is the Manning coefficient, θ cr is the Shields number and J is the hydraulic gradient.

[0019] In some embodiments, S4 further includes establishing a two-dimensional mathematical coupling model of bank slope seepage-stress-strain multi-physics fields under the hydrothermal effects of a typical dangerous section of the embankment, setting simulation calculation conditions for embankment seepage at different time periods, so as to calculate the risk of embankment seepage danger at different time periods.

[0020] In some embodiments, the calculation formula for the seepage risk of the dike at different time periods is as follows:

[0021] Ice flow period:

[0022]

[0023] River closure period:

[0024]

[0025] River opening period:

[0026]

[0027] The calculation formula for the full-time embankment seepage risk is as follows:

[0028] SL = h(SL 1 ,SL 2 ,SL 3 )

[0029] Among them, g 1 , g 2 , g 3 Solve the process function for the numerical model, function k 1 , k 2 , k 3 To compare the permeability coefficients k in the horizontal and vertical directions of x and y at the same time in different dangerous sections of the embankment wx ,k wy , volumetric moisture content θ, soil expansion deformation ε, force balance safety factor F f , torque balance safety factor F m The difference function of h is the total water head, S p is the slope of the straight line passing through the midpoint of the volumetric water content function, ε v is the soil volume strain, u w is the pore water pressure, K ij is the unit percolation conduction matrix, M ijis the water volume matrix generated by unit head change, D ij ” is the water volume matrix generated by unit flow change, X is the shear force between soil strips, c' is the effective cohesion coefficient, is the effective internal friction angle, α”’ is the inclination angle of the bottom of the soil strip, N is the normal force at the bottom of the soil strip, W is the weight of the soil strip, D is the line load, T is the transient temperature of the soil, λ(θ) is the thermal conductivity, θ u is the volume content of unfrozen water in frozen soil, T f is the soil freezing temperature, B I is the solid-liquid ratio, which represents the ratio of the pore ice volume to the unfrozen water volume in frozen soil, θ I is the relationship between pore ice, unfrozen water and temperature in frozen soil, ε is the soil expansion deformation, K' is the shear strength of the soil, and ε i is the strain caused by thermal expansion.

[0030] In some embodiments, S5 further includes: constructing an evaluation index system for embankment scour or seepage during ice flood season, including M indicators, and obtaining a subjective weighting weight vector W 1 , and obtain the objective weight vector W 2 ;

[0031] The calculation formula of the subjective and objective combined weight vector is as follows:

[0032]

[0033] in, is the subjective weight vector or objective weight vector of each evaluation index 1, 2, ...M, T is the transpose;

[0034] The comprehensive weight w of the jth evaluation index weighted by subjective and objective combination j , the calculation formula is as follows:

[0035]

[0036] in, is the subjective weight of the j-th evaluation index, Objectively assign weight to the j-th evaluation indicator.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1) Construct and develop a function formula for calculating the comprehensive risk of dike scour and seepage during different periods of the ice flood season, which can scientifically identify and quantify the scour risk, seepage risk and comprehensive risk of scour and seepage encountered by dikes during different periods of the ice flood season, provide a scientific basis for the management of dike engineering disaster risks during the ice flood season and the formulation of ice flood prevention and disaster reduction measures, and help to further improve the theoretical and technical level of dike disaster prevention during the ice flood season;

[0039] 2) Through theoretical analysis, numerical simulation, comprehensive evaluation and other technical means, the embankment scour risk model and seepage risk model were integrated to realize the embankment scour-seepage comprehensive risk assessment method suitable for different periods of the ice flood season. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the overall process of the comprehensive risk assessment method for embankment scour and seepage at different times during the ice flood season. DETAILED DESCRIPTION

[0041] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0042] like Figure 1 As shown, a method for evaluating the comprehensive risk of dike scour-seepage at different times during the ice flood season of the present invention comprises the following steps:

[0043] Step 1: Divide the ice flood season into different periods: According to the evolution of river ice conditions, the ice flood season is divided into three periods, namely, the floating ice period, the river closure period and the river opening period. The period from the beginning of ice flow to freezing is called the floating ice period; the period from the beginning of river closure to the freezing of the entire river is called the river closure period; the period from the melting of the upstream section to the opening of the river downstream to the full opening of the river is called the river opening period.

[0044] Step 2: Analyze the characteristics of ice-water conditions and embankment conditions in different time periods: Combine the three stages of the ice flood season obtained in step 1 to determine the characteristics of river ice conditions, water conditions, sediment transport, embankment seepage and frozen soil in each stage, explore the spatiotemporal variation laws and differentiation characteristics of the same characteristic indicators in each stage, and explore the driving correlation mechanism between the characteristic indicators in different stages of the ice flood season. Among them, ice condition characteristic indicators at least include ice body morphology, drift ice, ice cover, ice thickness, ice jams and ice dams, etc.; water condition characteristic indicators at least include changes in water level, flow rate and flow velocity; sediment transport is mainly manifested in sediment content and sediment transport rate; ice-water dynamic characteristic indicators at least include the movement law of ice in the river, its interaction with the water flow and its impact on the river (changes in the flow structure and hydrodynamic characteristics of the river, and the effect on the sediment transport capacity and riverbed morphology of the river); embankment engineering condition characteristic indicators at least include embankment seepage (seepage, pipe gushing, soil flow, etc.) and embankment frozen soil (soil volume expansion deformation, cracks, frozen soil thickness, permeability coefficient, etc.); through comparative analysis of different ice flood seasons (ice flow period, river closure period, river opening period) and different characteristic indicators (ice condition, water condition, sediment transport, embankment engineering condition), the influencing mechanism of the coupled driving of external conditions such as ice / water / sand on the evolution of the comprehensive risk of embankment scour-seepage is identified.

[0045] Step 3: Quantify the risk of dike scour at different stages of ice flood season, including the following processing:

[0046] Step 3.1, select typical dangerous sections of dikes and establish a two-dimensional mathematical coupling model of river channel-dike ice, water and sand: for different stages of ice flood season, combine the characteristics of ice conditions / water conditions / sand conditions (called ice-water-sand conditions) and dike conditions in different periods, select typical dangerous sections of dikes at different spatial positions from upstream to downstream, and establish a two-dimensional mathematical coupling model of river channel-dike ice, water and sand, which is a numerical model including a two-dimensional water condition / sand condition numerical calculation module, a river ice-water dynamics calculation module and a two-dimensional bank slope and riverbed scouring and erosion module, so as to quantitatively simulate the evolution process of scouring and erosion of riverbed and dike slope by ice cover, flowing ice and water-sand coupling movement;

[0047] Step 3.2, setting the boundary conditions for embankment scour simulation calculation at different periods during the ice flood period, including: considering the upstream water flow process (hourly flow or water level process), ice flow density and sediment content as the boundary conditions for embankment scour simulation calculation during the ice flow period; considering the upstream water flow process (hourly flow or water level process), ice cover thickness and sediment content as the boundary conditions for embankment scour simulation calculation during the river closure period; considering the river ice flood water level change process and sediment content as the boundary conditions for embankment scour simulation calculation during the river opening period;

[0048] Step 3.3, calculating the dike scour hazard index at different time periods, including: running the river-dike ice-water-sand two-dimensional mathematical coupling model according to the calculation boundary conditions set in step 3.2, and statistically analyzing the calculation results of the model to obtain the dike scour hazard index, using the side erosion distance ΔB at the slope foot as the scour risk index to judge the dike scour risk CS, and quantitatively analyzing the dike scour risk and its change process under the coupling effect of various calculation boundary conditions;

[0049] Step 3.4, establish the functional relationship for calculating the dike scour risk at different time periods, including: by analyzing the influence of different factors on the dike scour risk, identifying the main influencing indicators, constructing the theoretical formula for calculating the dike scour risk at each time period and the whole time period, and clarifying the nonlinear relationship between it and the influencing factors;

[0050] That is, during the ice flow period:

[0051] River closure period:

[0052] River opening period:

[0053] The calculation formula of dike scour risk during the whole period (from ice flow period to the end of river opening period) is as follows: CS = t (CS 1 ,CS 2 ,CS 3 )

[0054] Among them, f 1 、f2 、f 3 Solve the process function for the numerical model at different time periods, y 1 ,y 2 ,y 3 To compare the difference function of the side erosion distance ΔB of the slope foot in different dangerous sections of the embankment during the same period, ΔB 1 , ΔB 2 , ΔB 3 The side erosion distance of the slope foot at different periods, C l is the lateral scour coefficient, τ is the shear stress of nearshore flow, τ c is the anti-impact force of the slope soil, γ is the bulk density of the slope soil, Δt is the flood erosion time, h is the total water head, is the average value of the velocity components in the x and y directions based on the water depth, T ij is the lateral stress term T xx , T xy , T yy Any item in, S is the point source flow, ω * is the sediment settling velocity, S b1 is the bed load transport rate, S XY is the suspended sediment holding force, is the velocity of the flow under the ice sheet or ice sheet surface, c f is the drag coefficient, M is the Manning coefficient, θ cr is the Shields number and J is the hydraulic gradient.

[0055] The risk of dike scour during the whole period (from ice flow period to the end of river opening period) is: CS = t (CS 1 ,CS 2 ,CS 3 ), indicating that CS is the risk of dike scour in three periods CS 1 , CS 2 and CS 3 The functional relationship of can be used to determine the weight of the scour risk in different periods relative to the comprehensive scour risk of the embankment in the whole period through the subjective and objective combined weighting method, and then conduct quantitative analysis and evaluation of the scour risk. Function f 1 、f 2 、f 3 For the numerical model solution process, function y 1 ,y 2 ,y 3 In order to compare the differences in the side erosion distance ΔB of the slope foot in different dangerous sections of the embankment during the same period, an objective evaluation method is used to quantify the calculation, so as to obtain the embankment scour risk CS of a certain segment period. The meanings of the letters in the function expression are detailed in the following notes.

[0056] Step 4: Quantify the seepage risk of embankments at different times during the ice flood season, including the following processing:

[0057] Step 4.1, establish a two-dimensional mathematical coupling model of bank seepage-stress-strain multi-physics field under the water and heat effects of typical dangerous sections of embankments: for different periods of the ice flood season, combined with the characteristics of ice conditions, water conditions, temperature and embankment conditions in different periods, select typical dangerous sections of embankments at different spatial positions from upstream to downstream, and establish a two-dimensional mathematical coupling model of bank seepage-stress-strain multi-physics field. This model is a numerical model including a seepage-stability analysis module and a stress-strain analysis module. The two-dimensional mathematical coupling model of bank seepage-stress-strain multi-physics field is established. This model is a numerical model including a seepage-stability analysis module and a stress-strain analysis module, so as to quantitatively simulate the influence of the coupling effects of seepage, stress and strain on the seepage stability of the riverbed embankment bank slope;

[0058] Step 4.2, setting the conditions for embankment seepage simulation calculation at different time periods, including: considering the change process of ice flood water level and the change of external temperature at the corresponding time period, combining the actual ice conditions, water conditions, temperature and embankment working conditions of the embankment section, setting the calculation conditions of different temperature change processes and different water level change processes corresponding to different time periods, and using their hourly change processes as the conditions for embankment seepage simulation calculation at the corresponding time period;

[0059] Step 4.3, calculate the seepage hazard index of the embankment at different time periods, including: according to the frozen soil thickness change and embankment seepage process obtained by the model calculation, the permeability coefficient K in the x (horizontal) and y (vertical) directions is used wx , K wy , volumetric water content θ, soil expansion deformation ε, slope balance safety factor F f 、F m The seepage risk index composed of four indicators is used to judge the seepage risk SL of the levee, and quantitatively analyze the effect of various conditions on the seepage of the levee;

[0060] Step 4.4, establish the functional relationship for calculating the seepage risk of embankments in different time periods, including: by analyzing the influence of different factors on the seepage risk of embankments, identifying the main influencing indicators, constructing the theoretical formula for calculating the seepage risk of embankments in each time period and the whole time period, and clarifying the nonlinear relationship between it and the influencing factors;

[0061] Ice flow period:

[0062]

[0063] River closure period:

[0064]

[0065] River opening period:

[0066]

[0067] The calculation formula for the full-time embankment seepage risk is as follows:

[0068] SL = h(SL 1 ,SL 2 ,SL 3 )

[0069] Among them, g 1 , g 2 , g 3 Solve the process function for the numerical model, function k 1 , k 2 , k 3 To compare the permeability coefficients k in the x (horizontal) and y (vertical) directions of different dike sections at the same time wx ,k wy , volumetric moisture content θ, soil expansion deformation ε, force balance safety factor F f , torque balance safety factor F m The difference function of h is the total water head, S p is the slope of the straight line passing through the midpoint of the volumetric water content function, ε v is the soil volume strain, u w is the pore water pressure, K ij is the unit percolation conduction matrix, M ij is the water volume matrix generated by unit head change, D ij ” is the water volume matrix generated by unit flow change, X is the shear force between soil strips, c' is the effective cohesion coefficient, is the effective internal friction angle, α”’ is the inclination angle of the bottom of the soil strip, N is the normal force at the bottom of the soil strip, W is the weight of the soil strip, D is the line load, T is the transient temperature of the soil, λ(θ) is the thermal conductivity, θ u is the volume content of unfrozen water in frozen soil, T f is the soil freezing temperature, B I is the solid-liquid ratio, which represents the ratio of the pore ice volume to the unfrozen water volume in frozen soil, θ I is the relationship between pore ice, unfrozen water and temperature in frozen soil, ε is the soil expansion deformation, K' is the shear strength of the soil, and ε i is the strain caused by thermal expansion;

[0070] The risk of seepage in the dike during the whole period (from the ice flow period to the end of the river opening period) is: SL = h (SL 1 ,SL 2 ,SL 3 ), indicating that SL is the seepage risk SL of the dike in three periods 1 , SL 2 and SL 3The functional relationship of g can be used to determine the weight of seepage risk in different periods relative to the comprehensive seepage risk of the embankment in all periods through the subjective and objective combined weighting method, and then conduct quantitative analysis and evaluation of seepage risk. 1 , g 2 , g 3 For the numerical model solution process, function k 1 , k 2 , k 3 By comparing the permeability coefficients k in the x (horizontal) and y (vertical) directions of different dike sections at the same time period wx ,k wy , volumetric water content θ, soil expansion deformation ε, slope balance safety factor F f 、F m The difference is quantified by using the subjective and objective combined weighting method to obtain the levee seepage risk SL for a certain period. The meanings of the letters in the function expression are detailed in the following notes;

[0071] Step 5: Evaluate the comprehensive risk of erosion and seepage of dikes at different times during the ice flood season:

[0072] The present invention adopts the hierarchical analysis method to construct a multi-layer evaluation matrix of the comprehensive risk of dike scour-seepage in different periods during the ice flood season, adopts the subjective and objective combined weighting method to optimize the weighting, clarifies the risk weight allocation of dike scour risk and seepage risk in each period to the comprehensive risk, realizes the characteristic coupling of different periods and different risks to calculate the comprehensive risk ZH in different periods, compares and analyzes the characteristics of scour, seepage and comprehensive danger in different periods, and provides a scientific basis for the risk assessment and prevention and control of dikes during the ice flood season;

[0073] The present invention establishes the calculation function relationship of the comprehensive risk of dike scour-seepage under each period and the whole period, and clarifies the nonlinear relationship between it and the influencing factors. 1 =q(CS 1 ,SL 1 ); River closure period: ZH 2 =w(CS 2 ,SL 2 ); River opening period: ZH 3 =e(CS 3 ,SL 3 ); Full period (from ice flow period to the end of river opening period): ZH=r(ZH 1 ,ZH 2 ,ZH 3), indicating that ZH is a comprehensive functional relationship expression about CS and SL. Functions q, w, and e can be used to quantify the influence of scour risk CS and seepage risk SL on the comprehensive risk of dikes in different periods by using the subjective and objective combined weighting method, so as to obtain the comprehensive risk ZH of dike scour-seepage in a certain segment period.

[0074] The detailed instructions are as follows:

[0075] 1. The basis for dividing different periods of the ice flood season

[0076] Ice flow period: from the beginning of ice formation to the closure of the river, the duration varies from year to year, usually 5-20 days.

[0077] River closure period: Generally, the river is closed first at the downstream estuary due to low temperatures, and then gradually spreads upstream, with the length of the river closure increasing and the thickness of the ice layer increasing. However, sometimes due to a sudden drop in temperature, a relatively long river section may be closed at the same time. The start time of river closure is mostly concentrated in December to January of the following year.

[0078] River opening period: Every year in early spring, the weather turns warmer, and the temperature in the upper reaches rises above 0℃ first, and the ice begins to melt. Under the influence of thermal and hydraulic factors, it gradually moves downstream, the ice cover breaks up, and spring drift ice is formed. The river opening time in my country's cold regions is generally from mid-to-late February to late March.

[0079] 2. Principle of the two-dimensional mathematical coupling model of river channel-embankment ice-water-sand

[0080] (1) Hydrodynamic module

[0081] ① The hydrodynamic module of the present invention adopts a two-dimensional shallow water equation based on a numerical solution, the Reynolds average stress equation of an incompressible fluid integrated along the water depth, and obeys the Boussinesq hypothesis and the hydrostatic pressure hypothesis.

[0082] h=η+d

[0083] The basic equations include the continuity equation and the momentum equation as follows:

[0084] Continuity equation:

[0085]

[0086] Momentum equation:

[0087]

[0088] Where: is the average velocity based on water depth, t is time, x, y and z are Cartesian coordinates, η is the riverbed elevation; d is the still water depth, h = η + d is the total water head, u and v are the velocity components in the x and y directions, g is the gravitational acceleration, ρ is the water density, s xx 、s xy 、s yx 、s yy is the component of radiation stress, p a is the atmospheric pressure, ρ 0 is the relative density of water, S is the point source flow, u s 、v s is the flow rate of the source-sink water flow.

[0089] ② Lateral stress term T xx , T xy , T yy It includes viscous friction, turbulent friction, and differential advection, whose values ​​are estimated by the eddy viscosity formula based on the average velocity gradient of the water depth. The lateral stress term T xx , T xy , T yy The formula is as follows:

[0090]

[0091] Where: is the bottom shear stress, τ bx , τ by are the bottom shear stress in the x and y directions, c f is the drag coefficient; is the average velocity along the water depth direction, and M is the Manning coefficient.

[0092] (2) Sediment module

[0093] The movement of sediment in natural rivers includes two forms: suspended load movement and bed load movement. The riverbed deformation is affected by both suspended load and bed load movement. The movement of suspended sediment is affected by three factors: advection, diffusion and sedimentation.

[0094] ① The basic equation of suspended load non-steady unbalanced sediment transport is as follows:

[0095]

[0096] Where: h' is the water depth, S is the suspended sediment content, t is the time, p mod ,q mod are the components of the flux correction value in the x and y directions, ε x , ε y are the turbulent diffusion coefficients in the x and y directions respectively, α is the recovery saturation coefficient, which is related to the Rouse coefficient, ω * is the sediment settling velocity, SXY It is the suspended sediment carrying force.

[0097] ② The calculation formula for bed load sediment transport rate is as follows:

[0098]

[0099] Where: T SL is the dimensionless sediment transport coefficient, D * is the dimensionless sediment particle size parameter, s is the relative density of sediment, d 50 is the median particle size of sediment;

[0100]

[0101] Where: u f is the effective friction velocity, u f,c is the critical friction velocity, d 50 is the median particle size of sediment, s is the relative density of sediment, g is the acceleration of gravity, and V is the viscosity coefficient of water flow, which is approximately 10 -6 m 2 / s;

[0102]

[0103] Where: θ cr is the critical Shields number, s is the relative density of sediment, g is the gravitational acceleration, d 50 is the median particle size of sediment, V is the water flow velocity, and C is the riverbed roughness coefficient.

[0104] ③ The calculation formula of suspended sediment carrying capacity is as follows:

[0105] S XY =f·c a ·v·h'

[0106] Where: f represents the suspended sediment transport correction coefficient; c a It represents the suspended sediment content close to the bed surface; v represents the water flow velocity; h' represents the water depth.

[0107]

[0108] a=max(0.01h',2d 50 )

[0109] Where: a represents the relative thickness of the bottom bed, h' represents the water depth, Z represents the Rouse suspended sediment diffusion coefficient, d 50 is the median particle size of sediment, T SL is the dimensionless sediment transport coefficient, D * is the dimensionless sediment particle size parameter.

[0110] ④ The calculation formula of water flow sand entrainment force is as follows:

[0111] c e =c a [[[(2.21Z-6.41)Z+7.21]Z-3.95]Z+0.97](Z≤1)

[0112] c e =c a [[[(0.007Z-0.06)Z+0.22]Z-0.347]Z+0.22](1 <Z≤3)

[0113] c e =c a [[[(4·10 -6 Z-1.2·10 -4 )Z+1.4·10 -3 ]Z-7.67·10 -3 ]Z+0.018](Z>3)

[0114] ⑤The continuity equation of riverbed deformation is as follows:

[0115]

[0116] ΔS=αω * (cc e )

[0117] Where: n represents porosity, z represents the height of the riverbed bottom, S x , S y represents the sediment transport rate component in the x and y directions, ΔS represents the source and sink term, α is the recovery saturation coefficient, ω * represents sediment settling velocity, c represents sediment content, c e Indicates the sand-holding force.

[0118] (3) Ice-water dynamics calculation module

[0119] The surface stress of ice floes or ice sheets is caused by the roughness of ice and is determined by the law of secondary friction. By combining it with the basic governing equations of hydrodynamics, the movement process and dynamic characteristics of water and sand under the influence of ice floes and ice sheets can be obtained:

[0120]

[0121] Where: c f is the drag coefficient, is the velocity of flow beneath the surface of the icy stream or ice sheet. The friction velocity associated with the surface stress is given by:

[0122]

[0123] Where: is the depth-average velocity, and the drag coefficient can be determined by the Manning coefficient M.

[0124]

[0125] Among them, the Manning coefficient is estimated from the bed surface roughness length using the following method:

[0126]

[0127] (4) Bank slope and riverbed erosion module

[0128] Based on the two-dimensional hydrodynamic and sediment numerical calculation module and the ice-water dynamics impact module, combined with the characteristics of ice-water conditions and embankment conditions in different periods, the embankment riverbed scour and lateral erosion during the ice flood season are analyzed.

[0129] In order to quantify the influence of flow velocity and sediment content on the local scouring of dangerous dikes during ice floods, the scouring intensity of water flow is defined as α':

[0130]

[0131] Where: v represents the water velocity (m / s), s represents the sediment content (kg / m 3 ).

[0132] 1) The anti-impact force of the slope soil refers to the resistance of the soil to water erosion. The calculation formula is:

[0133] τ c =θ cr (ρ s -ρ)gD'

[0134]

[0135] Where: S , ρ are the density of sediment and water flow respectively, g is the acceleration of gravity, D' is the representative particle size of river bank soil, U * is the starting friction flow velocity, θ cr is the Shields number.

[0136] The functional relationship between Shields number and sediment particle size is as follows:

[0137] D * ≤4,θ cr =0.24(D * ) -1

[0138] 4 <D * ≤10,θ cr =0.14(D * ) -0.64

[0139] 10 <D * ≤20,θ cr =0.04(D * ) -0.10

[0140] 20 <D * ≤150,θ cr =0.013(D * ) 0.29

[0141] D * >150,θ cr =0.055

[0142] Where: D * It is a parameter related to the sediment particle size.

[0143] 2) The shear stress of nearshore flow is the main force causing bank slope scour, and the calculation formula is:

[0144] τ=ρ 0 h

[0145]

[0146] Where: τ is the shear stress of nearshore current, ρ 0 is the density of water, h is the water depth, J is the hydraulic slope, v is the water flow velocity, R is the hydraulic radius, the water depth value can be taken in the calculation of wide and shallow rivers, and n is the roughness.

[0147] 3. Calculation principle of side erosion distance ΔB at the slope foot

[0148] The Osman lateral erosion calculation model based on hydraulics and soil mechanics was used to analyze the lateral erosion of the earthen embankment slope under the scouring of ice floods, and the lateral erosion distance of the slope foot was calculated.

[0149] The calculation formula for lateral erosion distance is:

[0150]

[0151] Where: ΔB is the distance that the slope soil is eroded by flood in Δt time, C l is the lateral scour coefficient, generally C l =3.64x10 -4 , τ is the water flow scouring force, τ c is the impact resistance of the slope soil, and γ is the bulk density of the slope soil.

[0152] The applicable condition of the Osman lateral erosion model is the clay slope. The influencing factor m is added to the Osman formula to correct the lateral erosion rate of the slope under the action of water flow scouring, so as to reflect the lateral erosion characteristics of fine sand soil. The lateral erosion distance of the slope foot within Δt time is:

[0153]

[0154] 4. Principle of the two-dimensional mathematical coupling model of bank slope seepage-stress-strain multi-physics field

[0155] (1) Slope seepage-stability analysis module

[0156] 1) Saturated-unsaturated seepage finite element method

[0157] ① The saturated-unsaturated seepage finite element method is used to simulate the seepage process inside the slope soil. The basic equation for two-dimensional unsaturated soil seepage is:

[0158]

[0159] The basic equation for seepage in saturated soil is:

[0160]

[0161] in:

[0162]

[0163] Where: h(x,y,t) is the head function, i.e. the total head; k wx ,k wy are the permeability coefficients of unsaturated soil in the x (horizontal) and y (vertical) directions, k sx , k sy are the permeability coefficients of saturated soil in the x (horizontal) and y (vertical) directions respectively; ρ w is the density of the liquid (g / cm 3 ), g w is the water storage coefficient (gravitational acceleration, m / s 2 ), m w is the slope of the soil-water characteristic curve, which is related to the matrix force. α”, m, and n are curve fitting parameters. is matrix suction, S p is the slope of the straight line passing through the middle point of the volumetric water content function, θ is the volumetric water content, θ s ,θ r are saturated moisture content and residual moisture content respectively; S is saturation.

[0164] The initial conditions are expressed as:

[0165] h (t＝0) =h 0(x,y,t)

[0166] The boundary conditions include Γ 1 and Γ 2 , represent the first and second boundary conditions respectively. The first boundary conditions include head boundary conditions such as upstream and downstream water level boundary surfaces and free seepage boundary surfaces. The second boundary conditions refer to flow boundaries, and impermeable boundary surfaces also belong to the second boundary conditions.

[0167] The first type of boundary conditions:

[0168]

[0169] The second type of boundary conditions:

[0170]

[0171] Where: k n is the normal permeability coefficient, h is the hydraulic head, n is the normal direction outside the boundary surface, and q is the single-width flow rate.

[0172] The finite element calculation format of the basic seepage equation is:

[0173]

[0174] M ij '=C∫∫N i N j dxdy

[0175] D ij ”=∫∫ Γ2 N i N j dΓ

[0176] Where: [K] is the unit seepage conduction matrix, [M'] is the water volume matrix generated by unit head change, [D"] is the water volume matrix generated by unit flow change, {F 0} is the node water volume vector generated by the source and sink in the seepage field.

[0177] ② Unsaturated soil volume moisture content θ equation:

[0178] θ=β 0 ε v +ω 0 (u a -u w )

[0179]

[0180] Where: θ is the moisture content, ε v is the soil volume strain, u a 、u ware the pore gas pressure and pore water pressure, respectively, (Kpa), and u a =0, E is the elastic modulus (MPa), μ is the Poisson's ratio, H is the length in the volume change, and R is the width in the volume change.

[0181] The effective stress expression is:

[0182] σ'=σ-μ

[0183] Where: σ' is effective stress, σ is total stress, μ is pore water pressure

[0184] The stress-strain constitutive equation is:

[0185]

[0186] Where: W yb is the strain energy function, Ω is the complementary energy function, σ ij and ε ij are the stress tensor and the strain tensor respectively.

[0187] The above three equations are combined to derive the relationship between volumetric water content:

[0188]

[0189] Where: S e is the effective saturation.

[0190] Combining the above equation with the unsaturated soil seepage equation, the unsaturated soil seepage-stress coupling control equation is obtained as follows:

[0191]

[0192] 2) Morgenstern-Price limit equilibrium method for slope stability analysis

[0193] The Morgenstern-Price method is the only method that does not make assumptions in terms of slip surface morphology, static equilibrium requirements, and selection of redundant unknowns. It can simultaneously consider inter-strip shear force and normal force, and provide a flexible selection method for inter-strip force functions. Therefore, based on the finite element simulation of saturated-unsaturated seepage, the Morgenstern-Price method is used to perform stability analysis of dangerous slopes.

[0194] Two types of safety factors are defined according to force balance and moment balance. The soil is divided into strips, and the relationship between shear force and normal force between soil strips is established. The ratio of shear force and normal force between strips is changed through an iterative process. The safety factor that satisfies both moment balance and horizontal force balance conditions is the slope stability safety factor.

[0195] The relationship between the shear force and normal force between soil strips is expressed as:

[0196] X=Eλf(x)

[0197] Where: X represents the shear force between soil strips, λ represents the safety factor, E represents the normal force between soil strips, and f(x) represents the inter-strip force function.

[0198] Solve for the safety factor using the force balance equation:

[0199]

[0200] Where: F f is the force balance safety factor, F m is the moment balance safety factor, x, f, d, β, R, ω are all geometric parameters, c' is the effective cohesion coefficient, is the effective internal friction angle, μ is the pore water pressure, α”’ is the inclination angle of the bottom of the soil strip, N is the normal force at the bottom of the soil strip, W is the weight of the soil strip, and D is the line load.

[0201] (2) Dike water-heat-mechanical coupling stress-strain analysis module

[0202] 1) Temperature field control equation

[0203] Considering the two-dimensional water-heat coupling problem, according to Fourier's law, the phase change latent heat is treated as the heat source, and the differential equation of frozen soil heat conduction is:

[0204]

[0205] Where: is the differential operator, for two-dimensional problems it is T is the transient temperature of the soil (℃), t is the time (s), θ is the volumetric water content, θ I is the pore ice volume content, x and y are the horizontal and depth coordinates (m), ρ and ρ 1 is the density of soil and ice (kg / m 3 ), L is the latent heat of phase change, which is 334.5 kJ / kg, λ(θ) is the thermal conductivity (W / m·℃), and C(θ) is the volume heat capacity (J / kg·℃).

[0206] It should be noted that soil water consists of pore ice and pore water. u is the volume content of unfrozen water in frozen soil, ρ w is the density of water. Considering the different densities of ice and water, the volume moisture content of frozen soil is defined as θ = θ u +ρ l / ρ w ·θ Ⅰ , which is then used to calculate the thermal conductivity and volume heat capacity of frozen soil.

[0207] 2) Moisture field control equation

[0208] There is always unfrozen water in the soil under freeze-thaw conditions, and its migration follows Darcy's law. Considering the blocking effect of pore ice on the migration of unfrozen water, the differential equation for the migration of unfrozen water in unsaturated frozen soil is:

[0209]

[0210] Where: θ u is the volume content of unfrozen water in frozen soil, ρ w is the density of water (kg / m 3 ), k g is the permeability coefficient of unsaturated soil in the direction of gravity acceleration.

[0211] The relative saturation S of the frozen soil layer is:

[0212]

[0213] Where: θ r is the residual moisture content, θ s is the saturated moisture content.

[0214] 3) Dynamic equilibrium relationship of phase change

[0215] The frozen soil temperature field and moisture field contain three unknown quantities: temperature, pore ice volume content, and unfrozen water volume content. Therefore, a connection equation must be introduced to solve the water-heat coupling model, that is, to establish θ I ,θ u The relationship between T and T. Consider establishing this relationship equation through the dynamic equilibrium relationship of frozen soil phase change.

[0216] The empirical relationship expression of the volume content of unfrozen water in frozen soil is:

[0217]

[0218] Where: T f is the freezing temperature of soil (℃), w 0 is the initial moisture content of the soil (%), w u is the moisture content of unfrozen water at negative temperature (%), B is a constant, which is related to soil type and salt content. Generally, B can be selected from experience as 0.61 for sand, 0.47 for silt, and 0.56 for clay.

[0219] According to the concept of "solid-liquid ratio" (the ratio of the volume of pore ice in frozen soil to the volume of unfrozen water, denoted by B I ) Establish the connection equation:

[0220]

[0221] Where: The coefficient 1.1 is the density of water and ice ρ W / ρ I From the above formula, we can see that the solid-liquid ratio B I is a single-valued function of temperature.

[0222] The relationship equation between pore ice, unfrozen water and temperature in frozen soil is:

[0223] θ I =B I (T)·θ u

[0224] During the freezing process of soil, assuming that the soil particles and the gravel cushion layer are incompressible and are isotropic, the soil expansion deformation is calculated as follows:

[0225] ε=0.09(θ 0 -θ u )+1.09Δθ

[0226] Where: ε is the soil expansion deformation, θ 0 is the initial volume fraction, θ u is the volume fraction of unfrozen water, and Δθ is the volumetric moisture content of migrated water.

[0227] 4) Stress field control equation

[0228] The plasticity of soil is based on the Mohr-Coulomb theory:

[0229] K'=c+σtan(θ')

[0230] Where: K' is the shear strength of the soil, θ' is the internal friction angle of the soil, and c is the cohesion of the soil.

[0231] The Hoek-Brown criterion is used for rocks:

[0232]

[0233] Where: 1 is the maximum principal stress at failure (pressure is positive), σ 3 is the minimum principal stress of the rock mass acting on the rock sample, σ c is the uniaxial compressive strength of rock block, m' and s are empirical parameters.

[0234] The strain caused by thermal expansion is:

[0235] ε i =α””(θ”-θ 0 ”)

[0236] Where: α”” is the thermal expansion coefficient of the material, θ” is the instantaneous temperature (℃), θ 0 ” is the initial temperature (℃).

[0237] The volume frost heave rate is:

[0238]

[0239] The linear frost heave rate is:

[0240]

[0241] The thawing force can be calculated using the thermal expansion formula:

[0242]

[0243] 5) The temperature field differential equation, moisture field control equation, phase change dynamic equilibrium relationship equation and stress field control equation are combined to solve the set of equations for the water-heat-mechanical coupled stress-strain analysis of the levee.

[0244]

[0245] 5. On the subjective and objective combined weighting method

[0246] The subjective and objective combined weighting method adopted in the present invention is implemented as follows: construct an evaluation index system for dike scour or seepage during the flood season, assuming that it contains M indicators; use subjective weighting methods (hierarchy analysis method and fuzzy hierarchy analysis method) to calculate the weights of different indicators, calculate the average value of the indicator weights obtained by different subjective weighting methods, and obtain the subjective weighting weight vector W 1 ; Use objective weighting method (coefficient of variation method and entropy weight method) to calculate the weights of different indicators, calculate the average value of indicator weights obtained by different objective weighting methods, and obtain the objective weighting weight vector W 2 ;

[0247] The calculation formula of the subjective and objective combined weight vector is as follows:

[0248]

[0249] in, is the subjective weight vector or objective weight vector of each evaluation index 1, 2, ...M, T is the transpose;

[0250] Assuming that the comprehensive weights of subjective and objective weightings for calculating the jth flood season embankment scour or seepage risk evaluation index are: and The present invention adopts the product normalization idea of ​​the subjective and objective weighted average values ​​to obtain the comprehensive weight w of the jth evaluation index of the subjective and objective combined weighting j , the calculation formula is as follows:

[0251]

[0252] in, is the subjective weight of the j-th evaluation index, Objectively assign weights to the jth evaluation index

[0253] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions of the technical solution of the present invention by ordinary technicians in this field do not deviate from the essence and scope of the technical solution of the present invention.

Claims

1. A comprehensive risk assessment method for dike scour-seepage at different times during ice flood season, characterized in that: include: S1. According to the evolution of river ice conditions, the ice flood season is divided into three periods: floating ice period, river closure period and river opening period; S2. Analyze the characteristics of ice-water conditions and embankment conditions at different times during the ice flood season, at least determine the characteristics of river ice conditions, water conditions, sediment transport, embankment seepage and frozen soil in each stage, explore the temporal and spatial variation laws and differentiation characteristics of the same characteristic indicators in different time periods, and explore the driving correlation mechanism between the characteristic indicators at different times during the ice flood season. Through comparative analysis of different characteristic indicators at different times during the ice flood season, identify the influence mechanism of the coupling drive of ice / water / sand external conditions on the evolution of the comprehensive risk of embankment scour-seepage; ice condition characteristic indicators at least include ice body morphology, drift ice, and iceberg flow. , ice cover, ice thickness, ice jams and ice dams; water condition characteristic indicators at least include changes in water level, flow rate and flow velocity; sediment transport characteristic indicators at least include sediment content and sediment transport rate; ice-water dynamic characteristic indicators at least include the movement law of ice in the river, the interaction between ice and water flow and the impact on the river; embankment engineering condition characteristic indicators at least include embankment seepage and embankment frozen soil conditions; through comparative analysis of different ice flood periods and different characteristic indicators, identify the impact mechanism of the coupling drive of ice / water / sand external conditions on the evolution of the comprehensive risk of embankment scour-seepage; S3. Quantify the dike scour risk at different times during the ice flood season. The dike scour risk at different times is calculated based on the boundary conditions of the dike scour simulation at different times during the ice flood season. The river channel-dike ice-water-sand two-dimensional mathematical coupling model is run, and the calculation results of the model are statistically analyzed to obtain the dike scour hazard index. The side erosion distance of the slope foot in the dike scour hazard index is used as the dike scour risk; S4. Quantify the risk of levee seepage at different times during the ice flood season, including establishing a two-dimensional mathematical coupling model of bank slope seepage-stress-strain multi-physics field under the water-thermal action of typical levee dangerous sections, setting simulation calculation conditions for levee seepage at different times, so as to calculate the risk of levee seepage at different times; S5. Using the integrated embankment scour risk and embankment seepage risk, the embankment scour-seepage comprehensive risk at different times during the ice flood season is evaluated: the subjective weight vector W is used. 1 and the objective weight vector W 2 The subjective and objective combined weighting method is used to optimize the weighting, and the risk weights of dike scour risk and seepage risk in each period are allocated to the comprehensive risk degree, so as to achieve the characteristic coupling of different periods and different risks and calculate the comprehensive risk degree in different periods; Compare and analyze the scour, seepage and comprehensive hazard characteristics in different periods to evaluate the comprehensive risk of scour and seepage of dikes in different periods of the ice flood season.

2. The method for comprehensive risk assessment of dike scour and seepage during different periods of ice flood season according to claim 1 is characterized in that: The calculation formula for the dike scour risk at different time periods in S3 is as follows: Ice flow period: River closure period: River opening period: Among them, f1, f2, and f3 are the numerical model solution process functions at different time periods, y1, y2, and y3 are the difference functions for comparing the side erosion distance ΔB of the slope foot at the same time period in different dike dangerous sections, ΔB1, ΔB2, and ΔB3 are the side erosion distances of the slope foot at different time periods, and C l is the lateral scour coefficient, τ is the shear stress of nearshore flow, τ c is the anti-impact force of the slope soil, γ is the bulk density of the slope soil, Δt is the flood erosion time, h is the total water head, is the average value of the velocity components in the x and y directions based on the water depth, T ij is the lateral stress term T xx , T xy , T yy Any item in, S is the point source flow, ω * is the sediment settling velocity, S b1 is the bed load transport rate, S XY is the suspended sediment holding force, is the velocity of the flow under the ice sheet or ice sheet surface, c f is the drag coefficient, M is the Manning coefficient, θ cr is the Shields number and J is the hydraulic gradient.

3. The method for comprehensive risk assessment of dike scour and seepage during different periods of ice flood season according to claim 1 is characterized in that: The calculation formula for the seepage risk of dikes at different time periods in S4 is as follows: Ice flow period: River closure period: River opening period: Among them, g1, g2, and g3 are the numerical model solution process functions, and functions k1, k2, and k3 are the comparisons of the horizontal and vertical permeability coefficients k in the same period of time in different dike sections. wx ,k wy , volumetric moisture content θ, soil expansion deformation ε, force balance safety factor F f , torque balance safety factor F m The difference function of h is the total water head, S p is the slope of the straight line passing through the midpoint of the volumetric water content function, ε v is the soil volume strain, u w is the pore water pressure, K ij is the unit percolation conduction matrix, M ij is the water volume matrix generated by unit head change, D ij ” is the water volume matrix generated by unit flow change, X is the shear force between soil strips, c' is the effective cohesion coefficient, is the effective internal friction angle, α”’ is the inclination angle of the bottom of the soil strip, N is the normal force at the bottom of the soil strip, W is the weight of the soil strip, D is the line load, T is the transient temperature of the soil, λ(θ) is the thermal conductivity, θ u is the volume content of unfrozen water in frozen soil, T f is the soil freezing temperature, B I is the solid-liquid ratio, which represents the ratio of the pore ice volume to the unfrozen water volume in frozen soil, θ I is the relationship between pore ice, unfrozen water and temperature in frozen soil, ε is the soil expansion deformation, K' is the shear strength of the soil, and ε i is the strain caused by thermal expansion.

4. The method for comprehensive risk assessment of dike scour and seepage during different periods of ice flood season according to claim 1 is characterized in that: S5 further includes: constructing an evaluation index system for embankment scour or seepage during the ice flood period, including M indicators, and obtaining a subjective weighting weight vector W 1 , get the objective weight vector W 2 ; The calculation formula of the subjective and objective combined weight vector is as follows: in, is the subjective weight vector or objective weight vector of each evaluation index 1, 2, ...M, T is the transpose; The comprehensive weight w of the jth evaluation index weighted by subjective and objective combination j , the calculation formula is as follows: in, is the subjective weight of the j-th evaluation index, Objectively assign weight to the j-th evaluation indicator.

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