Optimization method of embankment breach row pile plugging scheme

Abstract

The invention relates to the technical field of emergency plugging of a embankment breach, discloses an optimization method of a embankment breach row pile plugging scheme, and aims to solve the problem of poor accuracy of an existing method. The scheme mainly comprises the following steps: judging a plugging difficulty level according to multi-dimensional parameters and a projection pursuit method based on a genetic algorithm; constructing a two-dimensional shallow water equation, and calculating breach water flow parameters through high-precision water flow simulation in the solving process; determining a dragging force coefficient and an inertia force coefficient through a least square method, and calculating the water flow impact force of the plugging structure of the embankment breach per unit length based on a Morison equation method; calculating an undrained shear strength standard value and a strain value when the maximum principal stress difference is half, and determining the ultimate bearing capacity of the row pile plugging structure based on the improved p-y curve; judging the bearing state of the row piles, optimizing the diameter and the pile distance of the steel pipe piles according to the bearing state of the row piles, and determining the pile point coordinates of the steel pipe piles. The accuracy of the row pile plugging scheme is improved.

Description

Technical Field

[0001] This invention relates to the field of emergency sealing technology for dike breaches, specifically to an optimized method for sealing dike breaches using pile-pile closure schemes. Background Technology

[0002] Dike engineering refers to a water-retaining structure in hydraulic engineering used for flood control and irrigation. Due to factors such as torrential rains during the flood season, there are significant safety hazards. Once a flood exceeding safe levels arrives, the dike may breach, causing severe loss of life and property to people downstream. Besides reinforcing dikes to prevent breaches, how to quickly seal breaches after they occur has become an important research issue. Emergency sealing of breaches can prevent the breach width from expanding further, prevent the floodwaters from continuing to rush and spread downstream, endangering houses and farmland, and reducing disaster losses.

[0003] Traditional dike breach sealing schemes using pile foundations have at least the following problems: First, the current assessment of sealing difficulty relies entirely on technicians visually inspecting or using simple tools to measure the breach width and water depth, judging the sealing difficulty based on experience. This is highly subjective, and the geological conditions depend on descriptions from local villagers or outdated geological reports, ignoring the layered characteristics of the soil. Second, when determining the dike breach sealing scheme, current technologies typically arrange piles at equal intervals according to the breach width, often resulting in excessively large pile spacing at the edges. Furthermore, the pile diameter is generally selected uniformly with no dynamic optimization of bearing capacity, leading to poor accuracy and a risk of material waste or structural instability. Summary of the Invention

[0004] This invention aims to solve the problem of poor accuracy in existing dike breach sealing schemes using pile foundations, and proposes an optimized method for dike breach sealing using pile foundations.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] An optimized method for sealing a breach in a dike using pile foundations, the method comprising:

[0007] Step 1: Obtain the multidimensional parameters of the initial river channel and dike breach. Based on the multidimensional parameters and the projection pursuit method based on the genetic algorithm, determine the difficulty level of sealing the dike breach.

[0008] Step 2: Construct two-dimensional shallow water equations based on the Godunov scheme, solve the Riemann problem at the grid boundary using the Roe scheme, improve spatial accuracy through the MUSCL scheme, introduce the TVD scheme to suppress numerical oscillations, and obtain the flow parameters of the breach section. During the solution process, the grid resolution is determined according to the difficulty level of sealing the dike breach.

[0009] Step 3: Based on the cross-sectional flow characteristics, the drag force coefficient and inertial force coefficient are determined by the least squares method. The water flow impact force per unit length of the dike breach sealing structure is calculated based on the flow parameters of the breach section and the Morison equation method.

[0010] Step 4: Input the initial pile parameters, input the geological condition parameters according to the local geological report of the breach, calculate the standard value of the undrained shear strength of the original clay and the strain value when the maximum principal stress difference is half in the triaxial test, and determine the ultimate bearing capacity of the pile sealing structure based on the improved py curve;

[0011] Step 5: Determine the bearing state of the piles based on the water flow impact force and ultimate bearing capacity, optimize the diameter and spacing of the steel pipe piles based on the bearing state, and determine the pile point coordinates of each steel pipe pile based on the embankment top coordinates calculated by the Beidou system.

[0012] Furthermore, based on the aforementioned multidimensional parameters and a projection pursuit method using a genetic algorithm, the difficulty level of sealing the dike breach is determined, including:

[0013] Step 11: Normalize each parameter in the multidimensional parameters;

[0014] Step 12: Construct a projection index function related to the overall density and local density, and optimize the projection direction vector based on a genetic algorithm to maximize the projection index function;

[0015] Step 13: Map the multidimensional parameters to one-dimensional projection values ​​based on the optimized projection direction vector, and determine the difficulty level of sealing the dike breach based on the one-dimensional projection values.

[0016] Furthermore, the matrix corresponding to the multidimensional parameters is as follows:

[0017] ;

[0018] The projection direction vector is:

[0019] ;

[0020] The one-dimensional projection value is:

[0021] ;

[0022] in, This represents the matrix corresponding to the multidimensional parameters. Represents the normalized th The first sample One parameter, , , Indicates the number of samples. Indicates the number of parameters. Represents the projection direction vector. Indicates the first One-dimensional projection value of each sample Indicates the first The weights of each parameter, Indicates matrix transpose;

[0023] The projection index function is as follows:

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] in, Represents the projection index function. Indicates overall density. Represents local density. The window width parameter represents the estimation of local scatter point density. Indicates the first The sample and the first The interval between the projected values ​​of each sample , This represents the step function.

[0030] Furthermore, the Roe scheme is used to solve the mesh boundary Riemann problem, including:

[0031] Step 21: Construct the average Roe value based on the states of the left and right elements on both sides of the element interface at the breach, as follows:

[0032] ;

[0033] If one side of the interface is a dry unit, then:

[0034] ;

[0035] in, This represents the average speed of the horizontal Roe. This represents the average vertical velocity of Roe. and Indicates the water depth of the left and right units. and This represents the horizontal velocity component of the left and right units. and This represents the vertical velocity components of the left and right elements. Indicates the equivalent wave velocity. Represents gravitational acceleration;

[0036] Step 22: Calculate three characteristic values ​​based on the average value of Roe, as follows:

[0037] ;

[0038] in, Represents the first eigenvalue. Represents the second eigenvalue. Indicates the third eigenvalue;

[0039] Step 23: Decompose the flux jump into a linear combination of different fluctuation modes and construct the characteristic matrix as follows:

[0040] , ;

[0041] in, Represents the left matrix, Represents the right matrix;

[0042] Step 24: Calculate the eigenvalues, as follows:

[0043] ;

[0044] in, , and This represents the flux jump coefficient in the characteristic space. This represents the jump size of the conserved variables in the left and right units. This represents the difference in water depth between the left and right units. , Indicates the difference in horizontal velocity components between the left and right units. , This represents the difference in vertical velocity components between the left and right elements. ;

[0045] Step 25: Calculate the interface flux based on the eigenvalues ​​and eigencoefficients, as follows:

[0046] ;

[0047] in, Indicates adjacent units and Interface throughput Representation unit flux, Representation unit flux, Indicates the first Flux jump coefficient Indicates the first 1 eigenvalue, Represents the right matrix The first in One right eigenvector, .

[0048] Furthermore, spatial accuracy is improved through the MUSCL format, and numerical oscillations are suppressed by introducing the TVD format, including:

[0049] The MUSCL scheme constructs the solution gradient of the current cell using the solution vectors of neighboring cells, while the TVD scheme suppresses numerical oscillations through a limiter function, as follows:

[0050] ;

[0051] ;

[0052] in, This represents the reconstructed left interface solution. Indicates the current unit The solution vector, Indicates adjacent units The solution vector, Indicates adjacent units The solution vector, This represents the limiter function.

[0053] Furthermore, the drag force coefficient and inertial force coefficient are determined using the least squares method, including:

[0054] The drag force coefficient and inertia force coefficient that minimize the error between the calculated force of the model and the actual fluid force are determined as follows:

[0055] ;

[0056] ;

[0057] in, Indicates the drag force coefficient. Indicates the inertial force coefficient. Represents the actual fluid force components, Indicates the phase angle. Indicates fluid density, Indicates the length of the cross section. Indicates the maximum flow rate. Indicates the average flow velocity. Indicates the periodic time.

[0058] Furthermore, the standard value of the undrained shear strength of the undisturbed clay and the strain value at half the maximum principal stress difference in the triaxial test were calculated, including:

[0059] Step 41: Calculate the undrained shear strength of the undisturbed clay layer by layer, as follows:

[0060] ;

[0061] ;

[0062] in, Indicates the first Undrained shear strength of layered clay Indicates the first The cohesion of layered clay, Represents the empirical coefficient. and They represent the first Layer and first The unit weight of layered clay, and They represent the first Layer and first The thickness of the clay layer, Indicates the first The internal friction angle of the clay layer, Indicates the depth of the piles embedded in the ground;

[0063] Step 42: Calculate the weighted average of the undrained shear strength of each clay layer to obtain the standard value of the undrained shear strength of the undrained clay, as follows:

[0064] ;

[0065] in, This represents the standard value of the undrained shear strength of undisturbed clay. Indicates the number of layers of undisturbed clay;

[0066] Step 43: Calculate the strain value at half the maximum principal stress difference, as follows:

[0067] ;

[0068] in, This represents the strain value when the difference between the maximum principal stresses is half.

[0069] Furthermore, the improved py curve is as follows:

[0070] ;

[0071] = ;

[0072] ;

[0073] in, This represents the ultimate horizontal resistance of the soil to the pile at different depths. Indicates the horizontal soil resistance of the pile. This indicates the lateral deformation of the pile. This represents the deformation at half the ultimate resistance. Indicates soil weight. Indicates the depth below the mud surface. Indicates the pile diameter or pile width.

[0074] Furthermore, the diameter and spacing of the steel pipe piles are optimized based on the bearing capacity of the pile group, including:

[0075] When the bearing capacity of the piles is too high, reduce the pile spacing or increase the diameter or wall thickness of the steel pipe piles. When the bearing capacity of the piles is too low, increase the pile spacing or decrease the diameter or wall thickness of the steel pipe piles until the bearing capacity of the piles reaches the preset bearing capacity, which is 50-70% of the ultimate bearing capacity.

[0076] Further, the coordinates of each steel pipe pile point are determined, including:

[0077] Step 51: When the bearing capacity of the pile bank reaches the preset bearing capacity, calculate the required number of steel pipe piles based on the breach width and initial pile spacing, as follows:

[0078] ;

[0079] in, This indicates the required quantity of steel pipe piles. Indicates the width of the ulcer. Indicates the initial pile spacing. This represents the floor function;

[0080] Step 52: Calculate the actual pile spacing based on the required number of steel pipe piles, as follows:

[0081] ;

[0082] in, Indicates the actual pile distance;

[0083] Step 53: Based on the actual pile spacing and the embankment top coordinates calculated by the Beidou system, output the pile point coordinates of each steel pipe pile at equal intervals.

[0084] The beneficial effects of this invention are as follows: The optimization method for the dike breach sealing scheme provided by this invention integrates multi-dimensional parameters and quantifies the sealing difficulty through genetic algorithm projection tracing, thus avoiding the subjectivity of experience; furthermore, this invention achieves dynamic optimization of the sealing scheme through precise modeling, dynamic optimization, and closed-loop control, thereby improving the accuracy of the dike breach sealing scheme and avoiding material waste and structural instability risks. In the precise modeling process, the grid resolution was determined according to the difficulty level of the closure, saving computational resources while ensuring calculation accuracy. During the solution process, high-precision water flow simulation (Godunov-Roe-MUSCL-TVD) was used to calculate the breach flow parameters, improving spatial accuracy, suppressing numerical oscillations, and ensuring the physical rationality of the flow parameters. By using the least squares method to invert the water flow impact force and correcting the Morison equation, the mechanical coefficients were matched with the actual situation, improving the accuracy of the water flow impact force calculation and thus improving the accuracy of the pile bearing state assessment. By improving the py curve to reflect the nonlinear response of the soil, the soil-water flow coupling was fully considered, improving the accuracy of the bearing capacity calculation and thus improving the accuracy of the pile bearing state assessment. During the dynamic optimization of the pile closure scheme, bearing capacity balance was used as a constraint for the coordinated optimization of pile diameter and pile spacing. Pile positions were output based on BeiDou positioning. BeiDou centimeter-level positioning of the output pile positions triggered a full-process replanning upon parameter mutations, achieving real-time response and further improving the accuracy of the pile closure scheme, as well as construction accuracy and efficiency, while saving materials. Attached Figure Description

[0085] Figure 1 A flowchart illustrating the optimized method for the dike breach sealing scheme using pile foundations provided in this embodiment;

[0086] Figure 2 A schematic diagram of the dike breach sealing scheme using pile-fill material provided in the embodiment;

[0087] Figure 3 A schematic diagram illustrating the construction of a two-dimensional shallow water equation for a dike breach, provided for an example.

[0088] Figure 4 A schematic diagram of the left and right intersection interfaces of the mesh reconstructed by the MUSCL method provided in the embodiment;

[0089] Figure 5 A schematic diagram of the TVD limiting function provided for the embodiment;

[0090] Figure 6 A schematic diagram illustrating the development trend of the Weihe River breach flow based on MATLAB numerical calculations, provided as an example.

[0091] Figure 7 A schematic diagram of the velocity wave and acceleration wave at the pile driving section of the Weihe River breach provided in the embodiment;

[0092] Figure 8 A schematic diagram of the water level change at the piling section of the Weihe River breach provided in this embodiment;

[0093] Figure 9 A schematic diagram of the time history curves of the maximum water flow impact force and bending moment of the piles provided for the embodiment;

[0094] Figure 10 A schematic diagram of the improved finite difference method for segmenting the Py curve provided in the embodiment;

[0095] Figure 11 A schematic diagram of the time history curve of the mud surface displacement response of the steel pipe pile provided for the embodiment;

[0096] Figure 12 A schematic diagram comparing the maximum bending moment and ultimate bending moment of the pile body provided for the embodiment;

[0097] Figure 13 This is a schematic diagram comparing the optimized results of the blocking scheme provided in the example.

[0098] Figure 14 A schematic diagram comparing the theoretical and simulated values ​​of the water flow impact force on the sealing structure provided in the embodiment;

[0099] Figure 15 A schematic diagram comparing different theoretical calculation values ​​with measured values ​​of Dagang Port in Zhenjiang, provided for the example. Detailed Implementation

[0100] To enable those skilled in the art to better understand the present invention, the technical solutions in this embodiment will be clearly and completely described below with reference to the accompanying drawings.

[0101] Because the current method of sealing dike breaches with piles usually involves arranging piles at equal intervals according to the width of the breach, it often results in excessively large pile spacing at the edges. Furthermore, the pile diameter is generally selected using a fixed diameter without dynamic optimization of bearing capacity, which leads to poor accuracy and can easily cause material waste or structural instability risks.

[0102] To improve the accuracy of the pile-blocking scheme, this invention proposes a technical solution. In this invention, multidimensional parameters of the initial river channel and dike breach are obtained. Based on these multidimensional parameters and a projection pursuit method using a genetic algorithm, the difficulty level of blocking the dike breach is determined. A two-dimensional shallow water equation is constructed based on the Godunov scheme, and the Riemann problem at the grid boundary is solved using the Roe scheme. The spatial accuracy is improved using the MUSCL scheme, and the TVD scheme is introduced to suppress numerical oscillations. The flow parameters of the breach section are obtained by solving the problem. During the solution process, the grid resolution is determined according to the difficulty level of blocking the dike breach. Based on the flow characteristics of the section, the drag is determined using the least squares method. The drag coefficient and inertia coefficient are calculated based on the water flow parameters of the breach section and the Morison equation method to determine the water flow impact force per unit length of the dam breach sealing structure. Initial pile parameters are input, and geological condition parameters are input based on the local geological report of the breach. The standard value of the undrained shear strength of the undisturbed clay and the strain value at half the maximum principal stress difference in the triaxial test are calculated. The ultimate bearing capacity of the pile sealing structure is determined based on the improved Py curve. The bearing state of the piles is judged based on the water flow impact force and ultimate bearing capacity. The diameter and spacing of the steel pipe piles are optimized based on the bearing state of the piles. The pile point coordinates of each steel pipe pile are determined based on the dam top coordinates calculated by the Beidou system.

[0103] Specifically, this invention first integrates multi-dimensional parameters and quantifies the sealing difficulty through genetic algorithm projection tracking. Then, it solves the breach flow parameters through high-precision water flow simulation, uses the least squares method to invert the impact force coefficient, and characterizes the nonlinear interaction between soil and piles based on an improved Py curve. Finally, it uses bearing capacity balance as a constraint to collaboratively optimize pile diameter and pile spacing. This invention reduces the error in difficulty grading and avoids subjective bias by replacing empirical judgment with genetic algorithm projection tracking; it accurately solves the Riemann problem using the Roe scheme, achieving second-order accuracy without oscillations through the MUSCL-TVD combination; it replaces standard empirical values ​​with least squares fitting and accurately reflects the progressive yielding characteristics of the soil based on the improved Py curve, improving the accuracy of impact force and bearing capacity calculations; and it collaboratively optimizes pile diameter and pile spacing with bearing capacity balance as a constraint, ensuring that material usage precisely matches the actual load. This avoids resource waste caused by conservative design while ensuring structural stability and improves the accuracy of the pile sealing scheme.

[0104] The technical solutions in this embodiment will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0105] Figure 1 A flowchart illustrating an optimized method for sealing a dike breach using pile foundations is provided. Please refer to [link / reference]. Figure 1 The method includes the following steps:

[0106] Step 1: Obtain the multidimensional parameters of the initial river channel and the breach in the dike. Based on the multidimensional parameters and the projection pursuit method based on the genetic algorithm, determine the difficulty level of sealing the breach in the dike.

[0107] In this embodiment, the multidimensional parameters of the initial river channel and the breach in the dike include river flow velocity, river depth, breach width, dike width, and dike height.

[0108] The projection pursuit method based on genetic algorithms finds the optimal one-dimensional projection of parameters while considering weights, and determines the blocking difficulty level accordingly. Specifically, it includes the following steps:

[0109] Step 11: Normalize each parameter in the multidimensional parameters.

[0110] In this embodiment, each parameter in the multidimensional parameters is normalized to obtain the matrix corresponding to the multidimensional parameters. For positive parameters with larger values, such as river flow velocity, river depth, and breach width, the normalization process is as follows:

[0111] ;

[0112] For negative parameters where smaller values ​​increase the difficulty of processing, such as dam width and dam height, the normalization process is as follows:

[0113] ;

[0114] The matrices corresponding to the multidimensional parameters obtained after normalization are as follows:

[0115] ;

[0116] in, This represents the matrix corresponding to the multidimensional parameters. Represents the normalized th The first sample One parameter, , , Indicates the number of samples. Indicates the number of parameters. Indicates the first digit before normalization. The first sample One parameter, Indicates the first The maximum value of each parameter. Indicates the first The minimum value of each parameter.

[0117] Step 12: Construct a projection index function related to the overall density and local density, and optimize the projection direction vector based on a genetic algorithm to maximize the projection index function.

[0118] In this embodiment, the projection index function is as follows:

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] ;

[0124] in, Represents the projection index function. Indicates overall density. Represents local density. The window width parameter represents the estimation of local scatter point density. Indicates the first The sample and the first The interval between the projected values ​​of each sample , This represents the step function.

[0125] The projection direction vector is:

[0126] ;

[0127] in, This represents the matrix corresponding to the multidimensional parameters. Represents the normalized th The first sample One parameter, , , Indicates the number of samples. Indicates the number of parameters. This represents the projection direction vector.

[0128] Step 13: Map the multidimensional parameters to one-dimensional projection values ​​based on the optimized projection direction vector, and determine the difficulty level of sealing the dike breach based on the one-dimensional projection values.

[0129] In this embodiment, the one-dimensional projection value is:

[0130] ;

[0131] in, Indicates the first One-dimensional projection value of each sample The larger the value, the higher the level of difficulty in blocking. Indicates the first The weights of each parameter, This indicates the matrix transpose.

[0132] In the above steps, the projection pursuit method optimizes the projection direction using a genetic algorithm, projecting multi-dimensional parameters into a one-dimensional space. Then, it calculates and maximizes the projection index function to distinguish different difficulty levels. Finally, it classifies the blocking difficulty level based on the one-dimensional projection value. Compared to empirical judgment, this reduces the error in difficulty classification and avoids subjective biases.

[0133] Step 2: Construct two-dimensional shallow water equations based on the Godunov scheme, solve the Riemann problem at the grid boundary using the Roe scheme, improve spatial accuracy using the MUSCL scheme, and introduce the TVD scheme to suppress numerical oscillations. Obtain the flow parameters of the breach section by solving the problem. During the solution process, determine the grid resolution according to the difficulty level of sealing the dike breach.

[0134] In this embodiment, the Roe scheme is used to solve the mesh boundary Riemann problem, including:

[0135] Step 21: Construct the average Roe value based on the states of the left and right elements on both sides of the element interface at the breach, as follows:

[0136] ;

[0137] If one side of the interface is a dry unit, then:

[0138] ;

[0139] in, This represents the average speed of the horizontal Roe. This represents the average vertical velocity of Roe. and Indicates the water depth of the left and right units. and This represents the horizontal velocity component of the left and right units. and This represents the vertical velocity components of the left and right elements. Indicates the equivalent wave velocity. Represents gravitational acceleration;

[0140] Step 22: Calculate three characteristic values ​​based on the average value of Roe, as follows:

[0141] ;

[0142] in, Represents the first eigenvalue. Represents the second eigenvalue. Indicates the third eigenvalue;

[0143] Step 23: Decompose the flux jump into a linear combination of different fluctuation modes and construct the characteristic matrix as follows:

[0144] , ;

[0145] in, Represents the left matrix, Represents the right matrix;

[0146] Step 24: Calculate the eigenvalues, as follows:

[0147] ;

[0148] in, , and This represents the flux jump coefficient in the characteristic space. This represents the jump size of the conserved variables in the left and right units. This represents the difference in water depth between the left and right units. , Indicates the difference in horizontal velocity components between the left and right units. , This represents the difference in vertical velocity components between the left and right elements. ;

[0149] Step 25: Calculate the interface flux based on the eigenvalues ​​and eigencoefficients, as follows:

[0150] ;

[0151] in, Indicates adjacent units and Interface throughput Representation unit flux, Representation unit flux, Indicates the first Flux jump coefficient Indicates the first 1 eigenvalue, Represents the right matrix The first in One right eigenvector, .

[0152] In the above steps, the grid resolution is determined by the closure difficulty level identified in step 1. Higher closure difficulty levels require finer grid cells, thus saving computational resources while maintaining computational accuracy. When solving the boundary Riemann problem based on the Roe scheme, the numerical flux at the cell interface is calculated through eigenvalue decomposition of the Roe average matrix, ensuring stable solutions for shock waves and discontinuities. The average state at the interface is represented by a Roe average value. Weighted averaging of the left and right cell states ensures that the interface flux satisfies conservation and stability. Complex flux jumps are decomposed into simple wave patterns to avoid numerical oscillations. When one side of the interface is a dry cell (water depth is zero), an arithmetic average is used to avoid numerical instability caused by a zero denominator. Combining the left and right flux averaging and eigenvalue decomposition results, a high-resolution interface flux is obtained, providing reliable flow parameter support for subsequent closure structure design.

[0153] In this embodiment, spatial accuracy is improved by using the MUSCL format, and numerical oscillations are suppressed by introducing the TVD format, including:

[0154] The MUSCL scheme constructs the solution gradient of the current cell using the solution vectors of neighboring cells, while the TVD scheme suppresses numerical oscillations through a limiter function, as follows:

[0155] ;

[0156] ;

[0157] in, This represents the reconstructed left interface solution. Indicates the current unit The solution vector, Indicates adjacent units The solution vector, Indicates adjacent units The solution vector, This represents the limiter function.

[0158] In the above steps, by modeling the hydrodynamics of the breach section, the flow parameters of the breach section, such as velocity, acceleration, and water surface height, are accurately solved. These flow parameters are then passed to step S3 for calculating the impact force of the flow. During the solution process, the MUSCL scheme improves the spatial accuracy to second order through linear reconstruction while avoiding numerical oscillations. Linear reconstruction utilizes the solution differences of adjacent elements to construct the solution gradient of the current element, and adjusts the gradient through a limiter to avoid overshoot or undershoot, ensuring the monotonicity of the solution. The TVD scheme suppresses numerical oscillations through a limiter function, avoiding non-physical oscillations and ensuring the stability of the solution. In this embodiment, the minmod limiter is selected, which dynamically adjusts the slope based on the sign of the differences between adjacent elements, balancing accuracy and robustness.

[0159] Step 3: Based on the cross-sectional flow characteristics, the drag force coefficient and inertial force coefficient are determined by the least squares method. The water flow impact force per unit length of the dike breach sealing structure is calculated based on the flow parameters of the breach section and the Morison equation method.

[0160] In this embodiment, the drag force coefficient and inertial force coefficient are determined by the least squares method, including:

[0161] The error between the actual fluid force components and the calculated fluid force is According to the least squares method, the drag force coefficient and the inertia force coefficient satisfy the following formula:

[0162] ;

[0163] The drag force coefficient and inertia force coefficient that minimize the error between the calculated force of the model and the actual fluid force are as follows:

[0164] ;

[0165] ;

[0166] in, Indicates the drag force coefficient. Indicates the inertial force coefficient. Represents the actual fluid force components, Indicates the phase angle. Indicates fluid density, Indicates the length of the cross section. Indicates the maximum flow rate. Indicates the average flow velocity. Indicates the periodic time.

[0167] In the above steps, the least squares method minimizes the error by optimizing the drag force coefficient and the inertial force coefficient, ensuring that the actual fluid force components are consistent with the calculated fluid force, thus achieving the scientific calibration of the drag force coefficient and the inertial force coefficient.

[0168] After obtaining the drag force coefficient and inertia force coefficient, substituting them into the Morison equation yields the water flow impact force per unit length of the dam breach sealing structure. The Morison equation is existing technology and will not be elaborated upon here. By using the least squares method to invert the water flow impact force and correcting the Morison equation, the mechanical coefficients are matched with the actual situation, improving the accuracy of the water flow impact force calculation and thus improving the accuracy of the pile bearing state assessment.

[0169] Step 4: Input the initial pile parameters, input the geological condition parameters according to the local geological report of the breach, calculate the standard value of the undrained shear strength of the original clay and the strain value when the maximum principal stress difference is half in the triaxial test, and determine the ultimate bearing capacity of the pile sealing structure based on the improved Py curve.

[0170] In this embodiment, the standard value of the undrained shear strength of undisturbed clay and the strain value at half the maximum principal stress difference in the triaxial test are calculated, including:

[0171] Step 41: Calculate the undrained shear strength of the undisturbed clay layer by layer, as follows:

[0172] ;

[0173] ;

[0174] in, Indicates the first Undrained shear strength of layered clay Indicates the first The cohesion of layered clay, Represents the empirical coefficient. and They represent the first Layer and first The unit weight of layered clay, and They represent the first Layer and first The thickness of the clay layer, Indicates the first The internal friction angle of the clay layer, Indicates the depth of the piles embedded in the ground;

[0175] Step 42: Calculate the weighted average of the undrained shear strength of each clay layer to obtain the standard value of the undrained shear strength of the undrained clay, as follows:

[0176] ;

[0177] in, This represents the standard value of the undrained shear strength of undisturbed clay. Indicates the number of layers of undisturbed clay;

[0178] Step 43: Calculate the strain value at half the maximum principal stress difference, as follows:

[0179] ;

[0180] in, This represents the strain value when the difference between the maximum principal stresses is half.

[0181] The above steps determine the undrained shear strength and strain value of the soil through layered calculations and weighted averaging. During the layered calculation process, the cohesion, internal friction angle, and overburden pressure of different soil layers are considered. The shear strength is calculated layer by layer and then adjusted using empirical coefficients. The contribution of overlying pressure is modulated, reflecting the deep dependence of shear strength.

[0182] In this embodiment, the improved py curve is as follows:

[0183] ;

[0184] = ;

[0185] ;

[0186] in, This represents the ultimate horizontal resistance of the soil to the pile at different depths. Indicates the horizontal soil resistance of the pile. This indicates the lateral deformation of the pile. This represents the deformation at half the ultimate resistance. Indicates soil weight. Indicates the depth below the mud surface. Indicates the pile diameter or pile width.

[0187] The improved Py curve accurately reflects the nonlinear response relationship between the lateral deformation of the pile and the soil resistance. Based on the improved Py curve, the ultimate bearing capacity of the pile sealing structure can be determined, and the ultimate bearing capacity of the soil at different depths on the pile can be accurately determined.

[0188] Step 5: Determine the bearing state of the piles based on the water flow impact force and ultimate bearing capacity, optimize the diameter and spacing of the steel pipe piles based on the bearing state, and determine the pile point coordinates of each steel pipe pile based on the embankment top coordinates calculated by the Beidou system.

[0189] In this embodiment, the diameter and spacing of the steel pipe piles are optimized according to the bearing state of the piles, including: when the bearing state of the piles is too large, the pile spacing is reduced or the diameter or wall thickness of the steel pipe piles is increased; when the bearing state of the piles is too small, the pile spacing is increased or the diameter or wall thickness of the steel pipe piles is decreased, until the bearing state of the piles reaches the preset bearing state, which is 50 to 70% of the ultimate bearing state.

[0190] Specifically, this embodiment uses bearing capacity balance as a constraint to collaboratively optimize pile diameter and pile spacing until the steel pipe piles reach a more reasonable stress state. This ensures that material usage accurately matches the actual load, avoiding resource waste caused by conservative design while maintaining structural stability, and improving the accuracy of the pile sealing scheme. Simultaneously, the Watch function monitors river channel and breach conditions. If parameters change, the sealing scheme is re-optimized through the above steps, achieving a closed loop from theoretical design to construction implementation, ensuring the efficiency and reliability of the pile sealing scheme.

[0191] In this embodiment, determining the coordinates of each steel pipe pile includes:

[0192] Step 51: When the bearing capacity of the pile bank reaches the preset bearing capacity, calculate the required number of steel pipe piles based on the breach width and initial pile spacing, as follows:

[0193] ;

[0194] in, This indicates the required quantity of steel pipe piles. Indicates the width of the ulcer. Indicates the initial pile spacing. This represents the floor function;

[0195] Step 52: Calculate the actual pile spacing based on the required number of steel pipe piles, as follows:

[0196] ;

[0197] in, Indicates the actual pile distance;

[0198] Step 53: Based on the actual pile spacing and the embankment top coordinates calculated by the Beidou system, output the pile point coordinates of each steel pipe pile at equal intervals.

[0199] In summary, the optimization method for the dike breach sealing scheme provided in this embodiment only requires obtaining initial river channel, dike breach parameters, and geological report parameters to effectively predict the sealing difficulty level of the dike breach. Based on the parameter conditions, it enables rapid calculation of the stress on the dike breach sealing structure and the bearing capacity of the piles, thereby realizing intelligent planning of the pile sealing scheme. It can also be optimized according to the dynamic changes in site conditions, enabling emergency decision-making, safety assessment, and real-time control during the sealing process, providing a basis for emergency sealing decisions for dike breaches.

[0200] The following will take the Weihe River “21.7” breach incident as an example, and describe the sealing scheme and optimization method in the embodiments of the present invention in conjunction with the implementation plan of the present invention.

[0201] Figure 2This is a schematic diagram of a piling and backfill sealing scheme for a dike breach. A piling machine advances from one bank to the top of the dike. Steel pipe piles, sandbags, and backfill are transported to the vicinity of the piling machine by a transport vehicle. The steel pipe piles are picked up, and the pile head is moved to the designated position using the Beidou positioning system on the pile head, and piling begins to the designated depth. Sandbags, gravel, and backfill are alternately dumped and compacted by the pile head to form a sealing dam body at the same height as the dike top. The piling machine is remotely controlled to continue advancing along the road on the top of the sealing dam body until the breach is sealed.

[0202] Figure 3 A schematic diagram of the two-dimensional shallow water equations for a dike breach is presented. The finite volume method is used to maintain quantity conservation within individual volumes. The two-dimensional flow mathematical model employs a structured mesh, which allows the control volumes to be rectangular. When the breach has a regular shape, rectangles facilitate determining the adjacency relationships between mesh cells, simplifying program design and improving computational efficiency. A square is chosen for each rectangular control volume and computational domain. In explicit computation, compared to triangular meshes, positively oriented meshes can reduce the time step and accelerate the computation. The mesh is extrapolated from the river channel region towards the breach and the outer planar region.

[0203] Figure 4 This diagram illustrates the reconstructed left and right interfaces of the mesh using the MUSCL method. The MUSCL method reconstructs the conserved variables on both sides of the element, and the reconstructed values ​​are used to replace the original values ​​on both sides during computation. and This improves the accuracy to the second order; however, areas with large water surface gradients may cause spurious numerical oscillations. Figure 5 The diagram illustrates the TVD constraint function. By introducing the TVD method, the total variation remains constant during numerical calculations, thus avoiding artificial oscillations in the numerical solution. This method is particularly suitable for cases of intermittent dike breaches.

[0204] Figure 6 To simulate the development of the Weihe River breach flow using MATLAB numerical calculations, the following parameters are input into MATLAB: levee crest width, river level, water level outside the breach, initial river velocity, and breach width. The development of the Weihe River breach flow is then simulated through numerical calculations, and the flow development process is calculated.

[0205] Figure 7 Schematic diagram of velocity wave and acceleration wave at the pile driving section of the Weihe River breach. Figure 8 This diagram illustrates the water surface changes at the piling section of the Weihe River breach. During the simulation of the breach's flow development, the average water surface height and average flow velocity of all grids at each moment at the piling section are recorded. Acceleration is calculated by differentiating the flow velocity with respect to time, yielding velocity waves, acceleration waves, and the time-history changes of the water surface, providing parameters for calculating the impact force of the water flow.

[0206] Figure 9 This is a schematic diagram of the time history curves of the maximum water flow impact force and bending moment of the pile deck. The initial pile spacing is set to 800mm, the pile diameter to be 0.3m, and the wall thickness to be 0.01m. After obtaining the velocity wave, acceleration wave, and water surface line of the pile driving section in the breach, the water flow impact force is calculated in MATLAB using the Morison equation, and then the time history curves of the maximum force and bending moment borne by the pile deck are calculated.

[0207] Figure 10 To improve the piecewise segmentation method of the finite difference method for Py curves, the differential equation of the pile body is solved using the finite difference method to determine the pile embedment depth. The pile body under the mud surface is divided into d segments, each segment being h in length. Two additional virtual points are extended upwards from the mud surface and downwards from the pile end, numbered from top to bottom as e=1, 2, 3…d+3, d+4, d+5, for a total of d+5 feature points, to facilitate the subsequent solution with sufficient unknowns.

[0208] Figure 11 This is a schematic diagram of the time history curve of the mud surface displacement response of a steel pipe pile. Figure 12 This is a schematic diagram comparing the maximum bending moment and ultimate bending moment of the pile body. The horizontal force and bending moment borne by the steel pipe pile are extracted every 0.4 seconds, and the displacement response time history curve of the steel pipe pile is obtained by calculating the displacement using an improved Py curve model. Based on the time history response, the pile displacement and bending moment under the most unfavorable condition are extracted and compared with the ultimate displacement and bending moment of the steel pipe pile.

[0209] Figure 13 The diagram shows the comparison of the results after the optimization of the sealing scheme. It is assumed that the water level at the site has risen to 1.5 times the original level due to continuous rainfall. After the water level rises, the bending moment of the pile body has exceeded the elastic limit bending moment, and the pile body has entered the plastic state. Through the optimization of the steel pipe pile size and wall thickness, when the wall thickness becomes 0.02m, the bearing capacity of the pile can reach 50-70% of the ultimate bearing capacity, which meets the optimization conditions. The breach sealing scheme of the pile can then be re-output.

[0210] Figure 14 This diagram illustrates the comparison between the theoretical calculation and simulated values ​​of the water flow impact force on the sealing structure. The comparison between the theoretical calculation and finite element simulation results shows that the theory and the results generally fit well, but the theoretical calculation results are slightly larger, with a maximum error of 10.53%. This proves that this embodiment can calculate the impact force of the sealing structure in the water flow within a certain error range.

[0211] Figure 15A schematic diagram comparing different theoretical calculation values ​​with measured values ​​at Zhenjiang Dagang is presented. Combined with data from on-site pile testing, the calculation results of horizontal displacement of steel pipe piles under the m method, NL method, standard py curve method, and improved py curve method are compared and analyzed. The improved py curve method has the best fitting effect and the smallest error, proving that the calculation results of the pile bearing capacity calculation method in this embodiment are relatively accurate.

Claims

1. An optimized method for sealing a breach in a dike using pile foundations, characterized in that, The method includes: Step 1: Obtain the multidimensional parameters of the initial river channel and dike breach. Based on the multidimensional parameters and the projection pursuit method based on the genetic algorithm, determine the difficulty level of sealing the dike breach. Step 2: Construct two-dimensional shallow water equations based on the Godunov scheme, solve the Riemann problem at the grid boundary using the Roe scheme, improve spatial accuracy through the MUSCL scheme, introduce the TVD scheme to suppress numerical oscillations, and obtain the flow parameters of the breach section. During the solution process, the grid resolution is determined according to the difficulty level of sealing the dike breach. Step 3: Based on the cross-sectional flow characteristics, the drag force coefficient and inertial force coefficient are determined by the least squares method. The water flow impact force per unit length of the dike breach sealing structure is calculated based on the flow parameters of the breach section and the Morison equation method. Step 4: Input the initial pile parameters, input the geological condition parameters according to the local geological report of the breach, calculate the standard value of the undrained shear strength of the original clay and the strain value when the maximum principal stress difference is half in the triaxial test, and determine the ultimate bearing capacity of the pile sealing structure based on the improved py curve; Step 5: Determine the bearing state of the piles based on the water flow impact force and ultimate bearing capacity, optimize the diameter and spacing of the steel pipe piles based on the bearing state, and determine the pile point coordinates of each steel pipe pile based on the embankment top coordinates calculated by the Beidou system.

2. The optimized method for the dike breach sealing scheme using pile foundations according to claim 1, characterized in that, Based on the aforementioned multidimensional parameters and a projection pursuit method using a genetic algorithm, the difficulty level of sealing the dike breach is determined, including: Step 11: Normalize each parameter in the multidimensional parameters; Step 12: Construct a projection index function related to the overall density and local density, and optimize the projection direction vector based on a genetic algorithm to maximize the projection index function; Step 13: Map the multidimensional parameters to one-dimensional projection values ​​based on the optimized projection direction vector, and determine the difficulty level of sealing the dike breach based on the one-dimensional projection values.

3. The optimized method for the dike breach sealing scheme using pile foundations according to claim 2, characterized in that, The matrices corresponding to the multidimensional parameters are as follows: ； The projection direction vector is: ； The one-dimensional projection value is: ； in, This represents the matrix corresponding to the multidimensional parameters. Represents the normalized th The first sample One parameter, , , Indicates the number of samples. Indicates the number of parameters. Represents the projection direction vector. Indicates the first One-dimensional projection value of each sample Indicates the first The weights of each parameter, Indicates matrix transpose; The projection index function is as follows: ； ； ； ； ； in, Represents the projection index function. Indicates overall density. Represents local density. The window width parameter represents the estimation of local scatter point density. Indicates the first The sample and the first The interval between the projected values ​​of each sample. , This represents the step function.

4. The optimized method for the dike breach sealing scheme using pile foundations according to claim 1, characterized in that, Solving the Riemann problem at mesh boundaries using the Roe scheme includes: Step 21: Construct the average Roe value based on the states of the left and right elements on both sides of the element interface at the breach, as follows: ； If one side of the interface is a dry unit, then: ； in, This represents the average speed of the horizontal Roe. This represents the average vertical velocity of Roe. and Indicates the water depth of the left and right units. and This represents the horizontal velocity component of the left and right units. and This represents the vertical velocity components of the left and right elements. Indicates the equivalent wave velocity. Represents gravitational acceleration; Step 22: Calculate three characteristic values ​​based on the average value of Roe, as follows: ； in, Represents the first eigenvalue. Represents the second eigenvalue. Indicates the third eigenvalue; Step 23: Decompose the flux jump into a linear combination of different fluctuation modes and construct the characteristic matrix as follows: ， ； in, Represents the left matrix, Represents the right matrix; Step 24: Calculate the eigenvalues ​​as follows: ； in, , and This represents the flux jump coefficient in the characteristic space. This represents the jump size of the conserved variables in the left and right units. This represents the difference in water depth between the left and right units. , Indicates the difference in horizontal velocity components between the left and right units. , This represents the difference in vertical velocity components between the left and right elements. ; Step 25: Calculate the interface flux based on the eigenvalues ​​and eigencoefficients, as follows: ； in, Indicates adjacent units and Interface throughput, Representation unit flux, Representation unit flux, Indicates the first Flux jump coefficient Indicates the first 1 eigenvalue, Represents the right matrix The first in One right eigenvector, .

5. The optimized method for the dike breach sealing scheme using pile foundations according to claim 4, characterized in that, Spatial accuracy is improved through the MUSCL format, and numerical oscillations are suppressed by introducing the TVD format, including: The MUSCL scheme constructs the solution gradient of the current cell using the solution vectors of neighboring cells, while the TVD scheme suppresses numerical oscillations through a limiter function, as follows: ； ； in, This represents the reconstructed left interface solution. Indicates the current unit The solution vector, Indicates adjacent units The solution vector, Indicates adjacent units The solution vector, This represents the limiter function.

6. The optimized method for the dike breach sealing scheme using pile foundations according to claim 1, characterized in that, The drag force coefficient and inertial force coefficient are determined using the least squares method, including: The drag force coefficient and inertia force coefficient that minimize the error between the calculated force of the model and the actual fluid force are determined as follows: ； ； in, Indicates the drag force coefficient. Indicates the inertial force coefficient. Represents the actual fluid force components, Indicates the phase angle. Indicates fluid density, Indicates the length of the cross section. Indicates the maximum flow rate. Indicates the average flow velocity. Indicates the periodic time.

7. The optimized method for the dike breach sealing scheme using pile foundations according to claim 1, characterized in that, The standard value of the undrained shear strength of undisturbed clay and the strain value at half the maximum principal stress difference in the triaxial test were calculated, including: Step 41: Calculate the undrained shear strength of the undisturbed clay layer by layer, as follows: ； ； in, Indicates the first Undrained shear strength of layered clay Indicates the first The cohesion of layered clay Represents the empirical coefficient. and They represent the first Layer and first The unit weight of layered clay, and They represent the first Layer and first The thickness of the clay layer, Indicates the first The internal friction angle of the clay layer, Indicates the depth of the piles embedded in the ground; Step 42: Calculate the weighted average of the undrained shear strength of each clay layer to obtain the standard value of the undrained shear strength of the undrained clay, as follows: ； in, This represents the standard value of the undrained shear strength of undisturbed clay. Indicates the number of layers of undisturbed clay; Step 43: Calculate the strain value at half the maximum principal stress difference, as follows: ； in, This represents the strain value when the difference between the maximum principal stresses is half.

8. The optimized method for the dike breach sealing scheme using pile foundations according to claim 7, characterized in that, The improved py curve is as follows: ； = ； ； in, This represents the ultimate horizontal resistance of the soil to the pile at different depths. Indicates the horizontal soil resistance of the pile. This indicates the lateral deformation of the pile. This represents the deformation at half the ultimate resistance. Indicates soil weight. Indicates the depth below the mud surface. Indicates the pile diameter or pile width.

9. The optimized method for the dike breach sealing scheme using pile foundations according to claim 1, characterized in that, Optimize the diameter and spacing of steel pipe piles based on the bearing capacity of the pile bank, including: When the bearing capacity of the piles is too high, reduce the pile spacing or increase the diameter or wall thickness of the steel pipe piles. When the bearing capacity of the piles is too low, increase the pile spacing or decrease the diameter or wall thickness of the steel pipe piles until the bearing capacity of the piles reaches the preset bearing capacity, which is 50-70% of the ultimate bearing capacity.

10. The optimized method for the dike breach sealing scheme using pile foundations according to claim 9, characterized in that, Determine the coordinates of each steel pipe pile point, including: Step 51: When the bearing capacity of the pile bank reaches the preset bearing capacity, calculate the required number of steel pipe piles based on the breach width and initial pile spacing, as follows: ； in, This indicates the required quantity of steel pipe piles. Indicates the width of the ulcer. Indicates the initial pile spacing. This represents the floor function; Step 52: Calculate the actual pile spacing based on the required number of steel pipe piles, as follows: ； in, Indicates the actual pile distance; Step 53: Based on the actual pile spacing and the embankment top coordinates calculated by the Beidou system, output the pile point coordinates of each steel pipe pile at equal intervals.

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