A method for determining the finite displacement of a high-pile wharf structure under the condition of horizontal load and damage to a foundation pile

Abstract

The application provides a high-pile wharf structure finite displacement determination method for pile damage under horizontal load condition, and belongs to the technical field of wharf construction. The application collects geometric parameters and foundation soil parameters of the high-pile wharf structure, determines the group pile effect coefficient initial value under the complete pile state, establishes the mapping relationship between the damage area ratio and the cross-section effective bending stiffness reduction ratio according to the cross-section three-part superposition rule, reconstructs the multi-pile damage stiffness evolution with the aid of artificial intelligence, deduces the dynamic correction formula of the group pile effect coefficient of the pile top displacement and the group pile effect coefficient of the mud surface displacement under the damage state based on the equal displacement failure criterion, processes the whole system constant of the multi-pile simultaneous damage by using the damage influence multiplication coupling rule, substitutes the corrected coefficient into the total horizontal displacement formula of the pile top to form the load-displacement relationship curve, and carries out bidirectional calculation by taking the elastic limit displacement as the failure criterion, so that the technical problem that the horizontal displacement of the high-pile wharf structure under the multi-pile asymmetric damage working condition cannot be accurately calculated is solved.

Description

Technical Field

[0001] This invention belongs to the field of wharf construction technology, and specifically relates to a method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions to prevent pile damage. Background Technology

[0002] High-pile wharf structures are subjected to horizontal loads such as ship impacts, wave impacts, and earthquakes during long-term service, making pile damage inevitable. Current technologies typically employ a fixed pile group effect coefficient method to address the horizontal load problem of high-pile wharves. This method superimposes the horizontal stiffness contributions of each pile with a fixed coefficient and then calculates the pile top displacement using elastic foundation beam theory or simplified formulas from specifications. Some studies also introduce finite element numerical simulation to predict displacement of typical intact structures, using the elastic limit displacement as the basis for structural safety evaluation. However, under conditions where multiple piles suffer asymmetric damage simultaneously, the degree of stiffness degradation varies among the damaged piles, leading to a dynamic redistribution of internal force transmission paths. The fixed pile group effect coefficient cannot reflect the coupled impact of this asymmetric stiffness change on the overall displacement. Furthermore, traditional methods often assume uniform stiffness reduction for damaged piles, neglecting the differences in the contribution of the compression damage zone, tension crack zone, and neutral axis adjacent zone to bending stiffness, resulting in insufficient physical basis for the reduction ratio. In other words, current technologies suffer from the technical problem of inaccurately calculating the horizontal displacement of high-pile wharf structures under conditions of asymmetric damage to multiple piles. Summary of the Invention

[0003] In view of this, the present invention provides a method for determining the finite displacement of a high-pile wharf structure with pile damage under horizontal loading conditions, which can solve the technical problem in the prior art that the horizontal displacement of a high-pile wharf structure under multi-pile asymmetric damage conditions cannot be accurately calculated.

[0004] This invention is implemented as follows: This invention provides a method for determining the finite displacement of a high-pile wharf structure with pile damage under horizontal loading conditions, comprising the following steps:

[0005] Collect structural geometric parameters and soil parameters of the pile-side foundation of the high-pile wharf;

[0006] Determine the initial values ​​of the pile top displacement group pile effect coefficient and the mud surface displacement group pile effect coefficient under the complete pile state. The pile top displacement group pile effect coefficient is taken within the preset range, and the mud surface displacement group pile effect coefficient is calibrated based on the proportional relationship between the elastic limit horizontal load and the elastic limit displacement.

[0007] The damage area ratio of each damaged pile is obtained. Based on the three-part superposition rule of the cross-section compression damage zone, tension cracking zone and neutral axis adjacent zone, the effective bending stiffness reduction ratio of the damaged pile cross-section is calculated. The mapping relationship between the damage area ratio and the structural stiffness degradation is constructed. The topological evolution model of the mechanical conservation residual dense jump graph is used to assist in the reconstruction of the multi-pile damage stiffness evolution.

[0008] The pile top displacement group pile effect coefficient and mud surface displacement group pile effect coefficient are dynamically corrected based on the damage area ratio. When multiple piles are damaged at the same time, the damage influence multiplication coupling law is used to calculate the overall damage group pile effect coefficient. When the damage area ratio reaches the complete damage threshold, the group pile effect coefficient of the subsystem composed of the remaining intact piles is recalibrated.

[0009] Substitute the pile top displacement group pile effect coefficient and mud surface displacement group pile effect coefficient under the damaged state into the pile top displacement formula to calculate the total horizontal displacement of the pile top under each load level and form a load-displacement relationship curve.

[0010] Using the elastic limit displacement as the failure criterion, and combining the load-displacement relationship curve, a two-way calculation is performed. The total horizontal displacement at the top of the pile can be obtained from the given horizontal load, or the finite displacement of the structure under the damage condition can be calculated from the elastic limit displacement.

[0011] The structural geometric parameters specifically include the inclined pile inclination angle, cross-sectional moment of inertia, elastic modulus, cross-sectional area, outer side length of the cross-section, inner side length of the cross-section, and length of the free segment of each pile; the pile side foundation soil parameters specifically include the horizontal resistance coefficient proportionality coefficient, property conversion coefficient, and pile influence coefficient.

[0012] Specifically, the pile top displacement caused by the deformation of the pile body above the mud surface is calculated using the pile top displacement group pile effect coefficient, elastic limit horizontal load, section moment of inertia, elastic modulus, inclined pile inclination angle, number of straight piles, number of inclined piles, and calculated pile length. The calculated pile length is determined by the sum of the free section length and the embedment point depth, and the embedment point depth is determined by the product of the single pile horizontal load and the outer side length of the section. The single pile horizontal load is first evenly distributed according to the number of piles, and then iteratively corrected according to the bending stiffness of each pile to obtain the final distribution value.

[0013] Specifically, the total displacement of the mud surface is calculated using the mud surface displacement group pile effect coefficient, elastic limit horizontal load, pile deformation coefficient, weighted pile length, weighted moment of inertia, number of straight piles, number of inclined piles, and inclined pile coefficient; the pile deformation coefficient is determined by the horizontal resistance coefficient proportionality coefficient, calculated width, and cross-sectional moment of inertia; and the inclined pile coefficient is determined by the inclined pile inclination angle, cross-sectional moment of inertia, cross-sectional area, and calculated pile length.

[0014] Specifically, the calibration of the mud surface displacement group pile effect coefficient is obtained by dividing the difference between the elastic limit displacement and the pile top displacement caused by the deformation of the pile body above the mud surface by the total mud surface displacement; the elastic limit displacement is taken as a multiple of the elastic limit displacement coefficient of the outer side length of the cross section; the reference value of the elastic limit displacement coefficient is 0.8.

[0015] Specifically, the three-zone superposition rule divides the cross-section into a compressive damage zone, a tensile cracking zone, and a neutral axis proximity zone. The damage reduction contribution of each zone to the cross-section's moment of inertia is calculated separately. Based on the superposition principle of structural mechanics, the total effective bending stiffness of the cross-section after damage is obtained, and its ratio to the initial bending stiffness in the undamaged state is used as the reduction ratio. For hollow square piles, the stiffness reduction reference value is 71% when the bending moment zone is completely damaged, and 29% when the shear force zone is completely damaged. For inclined piles, the damage area ratio and stiffness reduction ratio are determined in a one-to-one relationship.

[0016] Specifically, the mechanical conservation residual dense jump graph topology evolution model abstracts the high-pile wharf structure into a weighted directed graph, where nodes represent pile top nodes and mud surface nodes, and directed edge weights represent the reduced bending stiffness of the piles. The hidden layer uses a physical constraint operator constructed based on the differential equation of pile bending deformation, and dynamically determines the feature transmission path based on the residual of internal force balance at the nodes through gated routing. An internal long-span residual dense jump matrix is ​​constructed to splice shallow internal force features and deep displacement features in the channel dimension. When the internal force balance error exceeds the adaptive threshold, the hidden layer dynamic backtracking mechanism is triggered to correct the stiffness matrix weights in reverse.

[0017] The mechanical conservation residual dense jump graph topology evolution model is embedded with a multi-pile damage stiffness evolution reconstruction algorithm based on graph theory network flow. Specifically, the equivalent bending stiffness reduction rate of the damaged section is used as the upper limit of the network flow capacity. The redistribution path of internal forces among the piles is determined by calculating the maximum flow and minimum cut of the whole graph. The routing selection weight of the hidden layer of the neural network is updated according to the unbalance of the graph nodes. The neuron connection strength is updated in real time in each iteration to ensure the convergence of stiffness evolution.

[0018] The mechanical conservation residual dense jump graph topology evolution model sets a stiffness routing allocation function, specifically calculating the comprehensive routing index based on the maximum flow value, minimum cut value, and mean value of internal force balance residuals of the entire graph. The gating routing weight is dynamically adjusted based on the comparison results of the comprehensive routing index with low stiffness threshold, medium stiffness lower limit threshold, medium stiffness upper limit threshold, and high stiffness threshold. The reference values ​​for the low stiffness threshold, medium stiffness lower limit threshold, medium stiffness upper limit threshold, and high stiffness threshold are 0.6, 0.6, 1.2, and 2.0, respectively.

[0019] Specifically, the dynamic correction is based on the equal displacement failure criterion, which makes the expression for the total displacement at the pile top under the damaged state equal to the expression for the displacement under the intact state. This leads to the derivation of correction formulas for the pile top displacement group effect coefficient and the mud surface displacement group effect coefficient under the damaged state, with respect to the moment of inertia of the damaged pile section, the elastic limit horizontal load of the damaged pile, the pile length of the damaged pile, the proportional coefficient of the horizontal resistance coefficient of the foundation soil of the damaged pile, and the inclined pile coefficient of the damaged pile. The coefficients of the correction formulas are obtained through regression analysis of multiple sets of numerical simulation working conditions.

[0020] The normalized pile top displacement group pile effect coefficient and the damage area ratio are expressed as a quadratic polynomial for straight piles and bearing inclined piles, and as a linear form for bearing inclined piles; the normalized mud surface displacement group pile effect coefficient and the damage area ratio are expressed as a quadratic polynomial for both straight piles and inclined piles.

[0021] Specifically, the damage effect multiplication coupling rule involves calculating the pile top displacement group pile effect coefficient and the mud surface displacement group pile effect coefficient when each individual pile is damaged independently, multiplying the corresponding coefficients of each individual pile in sequence to obtain the overall group pile effect coefficient when multiple piles are damaged simultaneously; when the damage area ratio reaches the complete damage threshold, the subsystem composed of the remaining intact piles is regarded as a new complete structure, and the group pile effect coefficient is recalibrated; the reference value of the complete damage threshold is 100%.

[0022] The mud surface displacement group pile effect coefficient is also determined by a regression formula that introduces the pile missing quantity indicator variable and the same-side interaction term, in order to reflect the additional impact of asymmetric damage on the group pile effect. The specific regression coefficient is obtained by fitting numerical simulation statistical data.

[0023] Specifically, the training of the mechanical conservation residual dense jump graph topology evolution model employs a physical constraint loss function, which is a weighted superposition of the data fitting term and the residual term of the pile bending differential equation. The optimizer uses an adaptive moment estimation algorithm, and the learning rate decays according to a cosine annealing strategy. Training stops when the validation set loss does not decrease for several consecutive rounds, and the weights corresponding to the optimal validation set loss are used as the final model parameters. The weights of the physical residual term are initially set at the beginning of training and gradually increased to the termination weight value with each training round. The reference ratio between the initial weight value and the termination weight value is 1:1 to 1:3.

[0024] Specifically, the orthogonal decoupling of the third-order tensor in the mechanical conservation residual dense jump graph topology evolution model involves constructing a three-dimensional tensor from the streaming multi-channel sensor data according to its physical meaning, and performing singular value decomposition along the geometric dimension, load dimension, and damage state dimension to achieve mutual decoupling of information in the three dimensions. The training dataset uses different pile type parameters, different combinations of free segment lengths of bank slopes, different damage area ratios, and different horizontal load conditions as the parameter space. The reference value for the division ratio of the training set, validation set, and test set is 7:1.5:1.5.

[0025] This invention establishes a mapping relationship between the damage area ratio and the reduction ratio of the effective bending stiffness of the three-zone cross-section, derives a dynamic correction formula for the pile group effect coefficient under damage conditions using the equal displacement failure criterion, and utilizes the damage effect multiplication coupling law to handle the coupling effect of simultaneous damage to multiple piles, thus solving the defect that a fixed pile group effect coefficient cannot reflect asymmetric stiffness degradation. Since the damage coefficients of each individual pile are derived from physical principles, the multiplication coupling method preserves the independent physical meaning of each pile's damage, providing a clear mechanical basis for calculating the overall displacement under asymmetric damage to multiple piles. In summary, this invention solves the technical problem mentioned in the background art of the inaccurate calculation of the horizontal displacement of high-pile wharf structures under asymmetric damage conditions of multiple piles. Attached Figure Description

[0026] Figure 1 This is a flowchart of the method of the present invention.

[0027] Figure 2 This is a schematic diagram of the pile layout for a high-pile wharf. The numbers in the attached diagram are the pile numbers.

[0028] Figure 3 This is a schematic diagram of the partitioning of the moment of inertia of the cross section.

[0029] Figure 4 The figure shows a comparison of displacement-load curves between numerical simulation and formula calculation for all 10 piles of the high-pile wharf under damaged conditions, with all piles in a complete working state.

[0030] Figure 5 This is a comparison chart of the displacement-load curves calculated by numerical simulation and formula calculation for the damage condition of the No. 1 straight pile of the high-pile wharf under damaged conditions.

[0031] Figure 6 This is a comparison chart of the displacement-load curves calculated by numerical simulation and formula calculation for the damage condition of No. 10 inclined pile of the high-pile wharf under damaged conditions.

[0032] Figure 7 This is a comparison chart of the displacement-load curves between numerical simulation and formula calculation of the damage results of multiple piles in a high-pile wharf under damaged conditions. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0034] like Figure 1 The diagram shows a flowchart of a method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions, as provided by the present invention. This method includes the following steps:

[0035] S1. Collect the structural geometric parameters of the high-pile wharf, including the inclination angle of the inclined piles, the moment of inertia of the section, the elastic modulus, the cross-sectional area, the outer side length of the section, the inner side length of the section, and the length of the free section of each pile. Also collect the horizontal resistance coefficient, property conversion coefficient, and pile influence coefficient of the foundation soil on the pile side.

[0036] S2. Determine the initial values ​​of the pile top displacement group pile effect coefficient and the mud surface displacement group pile effect coefficient under the complete pile state. The pile top displacement group pile effect coefficient is taken in the range of 0.8 to 1.2, and the mud surface displacement group pile effect coefficient is calibrated according to the ratio of elastic limit horizontal load to elastic limit displacement.

[0037] S3. Obtain the damage area ratio of each damaged pile, calculate the effective bending stiffness reduction ratio of the damaged pile section according to the three-part superposition rule of the compression damage zone, tension cracking zone and neutral axis adjacent zone, and construct the mapping relationship between the damage area ratio and the structural stiffness degradation accordingly; use the mechanical conservation residual dense jump graph topology evolution model to assist in the reconstruction of the multi-pile damage stiffness evolution.

[0038] S4. Based on the damage area ratio, the pile top displacement group pile effect coefficient and mud surface displacement group pile effect coefficient under the condition of intact piles are dynamically corrected. When multiple piles are damaged at the same time, the damage influence multiplication coupling law is used to calculate the overall damage group pile effect coefficient. When the damage area ratio reaches 100%, the group pile effect coefficient of the subsystem composed of the remaining intact piles is recalibrated.

[0039] S5. Substitute the pile top displacement group pile effect coefficient and mud surface displacement group pile effect coefficient under the damaged state into the pile top displacement formula. Calculate the total horizontal displacement of the pile top under each load level by using the sum of the pile top displacement caused by the pile body deformation above the mud surface and the total mud surface displacement, thus forming a load-displacement relationship curve.

[0040] S6. Using the elastic limit displacement as the failure criterion, and combining the load-displacement relationship curve for bidirectional calculation: the total horizontal displacement at the top of the pile is obtained from the given horizontal load, or the finite displacement of the structure under the damage condition is calculated from the elastic limit displacement.

[0041] In step S1, the inclination angle of the inclined pile is determined based on the wharf design documents, with a typical value of 15°–30°. The outer and inner side lengths of the cross-section depend on the pile type; for straight piles, the typical outer side length is 0.45–0.65m, and the typical inner side length is 0.25–0.35m; for inclined piles, the typical outer side length is 0.40–0.60m, and the typical inner side length is 0.22–0.32m. The length of the free section of each pile varies due to the undulations of the bank slope and must be determined by actual measurement for each pile. The proportional coefficient of the horizontal resistance coefficient of the foundation soil on the pile side is based on the shear strength of the vane. according to Calculate the property conversion factor. Influence coefficient of pile The elastic modulus is calculated using a weighted average according to port engineering pile foundation specifications; The typical value is .

[0042] Among them, the pile top displacement group pile effect coefficient mentioned in step S2 The baseline value is 1.0, and the range is 0.8 to 1.2. The specific value is adjusted within this range according to the pile spacing, number of piles, and layout. The adjustment is based on the numerical simulation statistics of typical high-pile wharf pile group layout; the elastic limit displacement Based on the statistical results of numerical simulation of hollow square pile high pile wharf, the outer side length of the cross section is determined. 0.8 times, that is The pile top displacement caused by the deformation of the pile body above the mud surface Calculated by the following formula: ;in For the number of straight piles, For the number of inclined piles, For the elastic limit horizontal load, Calculate the pile length for the pile body. , For the embedding point depth, by calculate, For the horizontal load borne by a single pile, the horizontal load of a single pile is first distributed evenly according to the number of piles, and then according to the bending stiffness of each pile. The final allocation value is obtained by performing a weighted iterative correction; the total displacement of the mud surface Calculated by the following formula: ;in , , , , The pile deformation coefficient is... To calculate the width (using weighted values ​​during calculation). For force conversion factor, This is the coefficient for inclined piles (weighted values ​​are used in the calculation). Weighted pile lengths for all piles, The weighted moment of inertia for all piles; the mud surface displacement group pile effect coefficient. The calibration is performed using the load corresponding to the elastic limit displacement through numerical simulation. The calibration formula is as follows: .

[0043] Among them, the damage area ratio mentioned in step S3 Damage area Divide by the total cross-sectional area The value ranges from 0 to 100%. The three-zone superposition method divides the cross section into a compressive damage zone, a tensile cracking zone, and a neutral axis proximity zone. The damage reduction contribution of each zone to the cross section's moment of inertia is calculated separately. Based on the superposition principle of structural mechanics, the total effective bending stiffness of the cross section after damage is obtained. And its initial bending stiffness in the undamaged state The ratio is used as the reduction ratio; for hollow square straight piles, the cross section is divided into four rectangles on average. When the bending moment zone is completely damaged, the stiffness is reduced by about 71%, and when the shear force zone is completely damaged, the stiffness is reduced by about 29%; for inclined piles, the ratio of damaged area to stiffness reduction ratio is 1:1; the above reduction ratio values ​​are obtained through cross section partition geometric integration calculation and numerical simulation verification of multiple pile types; the simplified treatment of uniform stiffness reduction of the whole pile is applicable to the case of local bending damage at the pile top, because the length of the damaged section is much smaller than the calculated length of the pile body; the mechanical conservation residual dense jump graph topology evolution model assists in the reconstruction of multi-pile damage stiffness evolution in step S3, specifically acting on the adaptive correction of the equivalent bending stiffness of the damaged section and the dynamic redistribution calculation of the multi-pile damage stiffness field.

[0044] Among them, the pile top displacement group pile effect coefficient under the damage state described in step S4 Coefficient of effect of pile group with mud surface displacement Based on the derivation of the equal displacement failure criterion, assuming that both the damaged pile and the intact pile fail when they reach the preset elastic limit displacement, and setting the expression for the total displacement at the pile top under the damaged state to be equal to the expression for the displacement under the intact state, we get: ;in The moment of inertia of the damaged pile section, The results are numerical simulations of displacement failure in damaged piles. To the length of the damaged pile, This is the proportional coefficient of the horizontal resistance coefficient of the foundation soil along the pile side corresponding to the length of the damaged pile. The coefficient for damaged pile inclination; the normalized coefficient for pile top displacement group effect. Coefficient of effect of pile group with mud surface displacement Ratio of damage area The functional relationship between them, for both straight piles and bearing-pressure inclined piles, is as follows: For inclined piles under tension: For straight piles: For inclined piles: The coefficients in the above functional relationships are obtained through regression analysis of multiple sets of numerical simulation working conditions. The damage effect multiplication coupling rule is as follows: when multiple piles are damaged simultaneously, the pile top displacement group pile effect coefficient and mud surface displacement group pile effect coefficient for each individual pile damaged independently are calculated separately. Then, the corresponding coefficients of each individual pile are multiplied in turn to obtain the overall coefficient when multiple piles are damaged simultaneously. The coupling rule is based on the assumption that the damage effects of individual piles are independent of each other and is applicable to the working conditions of group piles with conventional pile spacing. When the damage area ratio of any pile reaches 100%, the subsystem composed of the remaining intact piles is regarded as a new complete structure, and the pile top displacement group pile effect coefficient and mud surface displacement group pile effect coefficient under the undamaged state are recalibrated according to step S2. The mud surface displacement group pile effect coefficient can also be determined by regression formula based on the pile missing working condition, which introduces the pile missing number indicator variable and the same-side interaction term to reflect the additional influence of asymmetric damage on the group pile effect. The specific regression coefficient is obtained by fitting numerical simulation statistical data.

[0045] Among them, the total horizontal displacement of the pile top mentioned in step S5 The calculation formula is: ;in This refers to the displacement of the pile top caused by deformation of the pile body above the mud surface. The total displacement of the mud surface is represented by the pile top displacement under damage conditions and the group pile effect coefficient. Coefficient of effect of pile group with mud surface displacement Substitute the formula described in step S2 into the calculation.

[0046] Among them, the elastic limit displacement mentioned in step S6 The method described in step S2 is used to determine the following: the two-way calculation is as follows: when the external horizontal load is known, the total horizontal displacement at the top of the pile is obtained from the load-displacement relationship curve; when the elastic limit displacement is known, the finite displacement of the structure under the damage condition is calculated by back-calculating from the load-displacement relationship curve.

[0047] The mechanical conservation residual dense jump graph topology evolution model is based on deep learning, abstracting the spatial structure of the high-pile wharf into a weighted directed graph. Nodes represent pile top nodes and mud surface nodes, and the weights of directed edges represent the reduced bending stiffness of the corresponding piles. In the pre-processing stage, the input sensor stream data is divided into geometric, load, and damage state dimensions through third-order tensor orthogonal decoupling. Third-order tensor orthogonal decoupling refers to constructing a three-dimensional tensor based on the physical meaning of the multi-channel sensor data and performing singular value decomposition along the three orthogonal dimensions to achieve mutual decoupling of the three dimensions of information, ensuring that the hidden layer features of each dimension do not interfere with each other. The hidden layer uses a physical constraint operator constructed based on the differential equation of pile bending deformation. Node features are conditionally jumped through gated routing during transmission. Gated routing dynamically determines whether a feature is transmitted through the current path based on the residual of internal force balance at the node. When the residual exceeds an adaptive threshold, it jumps to a bypass path. The network internally constructs a long-span residual dense jump matrix, directly concatenating the internal force characteristics of the upper-layer cross-section with the deep displacement characteristics through channel-dimensional splicing. This long-span residual dense jump matrix refers to a jump connection matrix spanning multiple hidden layers, where matrix elements are linear combination weights of corresponding inter-layer features. "Dense" means that each upper layer establishes jump connections with all lower layers. When the real-time predicted internal force balance error exceeds the adaptive threshold, a dynamic backtracking mechanism for the hidden layers is triggered, reversing the stiffness matrix weights. The adaptive threshold is automatically updated based on the exponential moving average of the internal force residuals in each iteration step. The model embeds a multi-pile damage stiffness evolution reconstruction algorithm based on graph theory network flow, abstracting the high-pile wharf structure as a weighted guided force graph. Nodes represent the connection points between the pile top and the mud surface, and edge weights represent the reduced bending stiffness of the foundation piles. When a single pile is damaged, the algorithm uses the reduction rate of the equivalent bending stiffness of the damaged section as the upper limit of the network flow capacity. It dynamically determines the redistribution path of internal forces among the piles by calculating the maximum flow and minimum cut of the entire graph. During the iteration process, the routing weights of the hidden layer of the neural network are updated based on the graph node imbalance, prompting the feature flow to shift to high-stiffness paths. The graph node imbalance is the ratio of the difference between the inflow and outflow internal forces of a node to the total flow of the node. The multi-pile damage stiffness evolution reconstruction algorithm transforms the evolution of structural internal force transmission paths into a network flow optimization problem. The neuron connection strength is updated in real time for each iteration to ensure the convergence of stiffness evolution. The activation feature transmission weights between neurons are dynamically allocated based on the gated routing residuals. The residual jump features between layers are weighted and aggregated by the channel dimension using a long-span residual dense jump matrix. The cyclic flow of data among graph nodes updates the upper limit of transmission capacity based on the maximum flow and minimum cut iteration results. Memory allocation adaptively adjusts the batch size based on the number of damaged nodes in each batch of input. Memory allocation dynamically plans the buffer based on the feature dimensions of each dimension after orthogonal decoupling of the third-order tensor. This model is compared with the damage area ratio. Moment of inertia of damaged pile section and elastic limit horizontal load Generate direct computational relationships, model output and This serves as the input parameter for the coefficient correction formula in step S4.

[0048] The specific steps for establishing the training dataset of the mechanical conservation residual dense jump graph topology evolution model include: using different pile type parameters, different combinations of free segment lengths of bank slopes, different damage area ratios, and different horizontal load conditions as the parameter space, using finite element numerical simulation software to batch generate data on the total horizontal displacement of the pile top, the total displacement of the mud surface, the distribution of internal forces in the cross section, and the elastic limit horizontal load under each condition; performing third-order tensor quantization on the data of each condition, dividing it into training set, validation set, and test set, with a ratio of 7:1.5:1.5; and labeling the damaged pile section moment of inertia, elastic limit horizontal load, and key node values ​​of the load-displacement relationship curve under the corresponding condition.

[0049] The training steps of the mechanical conservation residual dense jump graph topology evolution model specifically include: adopting a physical constraint loss function, which is composed of a weighted superposition of the data fitting term and the residual term of the pile bending differential equation. The weight coefficient is set to 1:1 in the early stage of training, and the weight of the physical residual term is gradually increased to 1:3 with the increase of training rounds to ensure that the mechanical conservation law is satisfied after the model converges; the optimizer adopts an adaptive moment estimation algorithm with an initial learning rate of The validation set loss decays to a certain value using a cosine annealing strategy. The batch size is adaptively set by the memory allocation module based on the current number of damaged nodes, ranging from 16 to 128. Training stops when the validation set loss does not decrease for 20 consecutive rounds, and the weights corresponding to the optimal validation set loss are used as the final model parameters.

[0050] The technical effects of the mechanical conservation residual dense jump graph topology evolution model are as follows: By embedding physical conservation laws into the network loss function and hidden layer operators, the model can still maintain internal force balance constraints when generalizing to unseen working conditions, avoiding physically unreasonable predictions in the extrapolation interval by purely data-driven models; the long-span residual dense jump matrix enables deep displacement features to directly obtain gradient information of shallow internal force features, effectively alleviating the problem of gradient vanishing in deep networks and improving the convergence speed and accuracy of displacement prediction in multi-pile damage scenarios; the graph theory network flow multi-pile damage stiffness evolution reconstruction algorithm transforms nonlinear stiffness evolution into a network flow optimization problem with clear physical meaning, enabling the model to have good generalization ability for multi-pile asymmetric damage scenarios, effectively overcoming the problem of deviation in traditional fixed pile group coefficient methods under multi-pile asymmetric damage.

[0051] The mechanically conserved residual dense jump graph topology evolution model designs a stiffness routing assignment function, which is based on the maximum flow value of the entire graph in the current iteration step. Minimum cut value of the whole graph and the mean value of internal force balance residuals The comprehensive routing index is calculated from three data points. The calculation formula is: ,in To prevent extremely small positive numbers from being divided by zero, the value is determined by numerical experiments, and the range is [range missing]. ;when At this time, the gated routing weights are tilted towards bypass jump paths, and the transmission ratio of residual jump connections is increased during hidden layer feature propagation to improve the model's sensitivity to low-stiffness damaged paths; when At this time, the gated route weights remain at the default allocation, and the hidden layer feature propagation is allocated equally between the normal path and the jump path (50% each). When the gating route weights are tilted towards the main path, the bypass hop ratio is reduced to suppress excessive characteristic disturbances under high-stiffness paths; when When the hidden layer dynamic backtracking mechanism is triggered, the stiffness matrix weights are forcibly corrected in reverse and the internal force balance residuals are reset to prevent the model from falling into local extrema under extreme load conditions. The above thresholds of 0.6, 1.2, and 2.0 were determined by statistical analysis of the distribution of routing exponents under different damage conditions in the training set and multiple rounds of ablation experiments. The specific method is as follows: using 0.4, 0.6, 0.8, 1.0, 1.2, 1.5, 2.0, and 2.5 as candidate thresholds, the number of convergence rounds and prediction errors of internal force residuals under each segmented strategy are statistically analyzed on the validation set, and the threshold combination that minimizes the comprehensive error of the validation set is taken as the final value.

[0052] The aforementioned third-order tensor orthogonal decoupling refers to constructing a three-dimensional tensor from the streaming multi-channel sensor data according to its physical meaning, and performing singular value decomposition along the three orthogonal dimensions to achieve mutual decoupling of information in the geometric dimension, load dimension, and damage state dimension. This allows for online lossless dimensionality reduction and multi-scale noise filtering of high-frequency streaming data at the memory layer, ensuring zero-blocking real-time throughput of transient data streams. The technical effects of third-order tensor orthogonal decoupling are as follows: by eliminating the linear correlation between the three-dimensional features through orthogonalization, each layer of the network only needs to process information in a single physical dimension, reducing the interference of hidden layer features, significantly improving the robustness and convergence stability of the model under high-frequency noise data, and simultaneously enabling high-dimensional streaming data to undergo effective dimensionality reduction before being input into the network, reducing the occupation of invalid features in GPU memory and RAM.

[0053] The technical effects of the proposed multi-pile damage stiffness evolution reconstruction algorithm based on graph theory network flow are as follows: it transforms the evolution of structural internal force transmission paths into a network flow optimization problem, accurately describes the internal force redistribution path under multi-pile damage through maximum flow minimum cut iteration, and overcomes the defect of traditional methods where the fixed path assumption cannot reflect the internal force flow phenomenon caused by damage; each iteration updates the edge weights and neuron connection strength in real time, making the stiffness evolution process have clear physical interpretability, while avoiding the computational path degradation problem caused by multi-pile asymmetric damage, and ensuring iterative convergence.

[0054] The technical effect of the damage effect multiplication coupling rule is as follows: by multiplying the independent damage coefficients of each single pile, the damage coupling calculation of multiple piles is realized. The calculation method is simple and the physical meaning is clear. It has high accuracy under the condition of pile group working with conventional pile spacing. It avoids the systematic deviation caused by ignoring the coupling effect in the traditional fixed pile group coefficient method in the multi-pile damage scenario. At the same time, it greatly reduces the calculation dimension compared with the full matrix coupling method, and is suitable for direct engineering application.

[0055] Optionally, this method also provides a computer-implemented system, wherein the computer is equipped with a readable storage medium storing program instructions. When the program instructions are run in the computer, they execute the above-described method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions. The computer is also connected to a sensor data acquisition module, which is used to write pile top displacement monitoring data and pile side foundation soil parameters to the readable storage medium in real time to support online inference of the mechanical conservation residual dense jump graph topology evolution model and dynamic updating of the damage group pile effect coefficient.

[0056] The specific implementation of step S1 involves collecting the structural geometric parameters and foundation soil parameters of each pile in the high-pile wharf through on-site surveys and review of design documents. The structural geometric parameters include the pile inclination angle, moment of inertia, elastic modulus, cross-sectional area, outer side length, inner side length, and free section length of each pile. Due to the undulating terrain of the wharf slope, the free section lengths of each pile vary and must be determined by on-site measurement for each pile. The foundation soil parameters include the horizontal resistance coefficient proportionality factor, property conversion factor, and pile influence factor, where the horizontal resistance coefficient proportionality factor is based on the vane shear strength. according to Calculate the property conversion factor. Influence coefficient of pile The displacement calculation is performed using weighted averages according to port engineering pile foundation specifications. The purpose of this step is to provide complete input parameters for subsequent steps; the completeness and accuracy of parameter acquisition directly affect the reliability of the displacement calculation results.

[0057] The specific implementation of step S2 is to determine the initial value of the pile group effect coefficient under the condition of a complete pile. The pile top displacement and pile group effect coefficient are then determined. The baseline value is 1.0, and the range is 0.8 to 1.2, adjusted within this range according to the pile spacing, number of piles, and arrangement. Elastic limit displacement. Take the outer side length of the cross section 0.8 times. The pile top displacement caused by pile deformation above the mud surface. The calculation of pile length and elastic limit horizontal load is based on the elastic modulus, moment of inertia of the section, inclination angle of the inclined pile, number of straight piles, number of inclined piles, pile length, and elastic limit horizontal load. The calculated pile length is determined by the sum of the free section length and the embedment point depth. The embedment point depth is based on the single pile horizontal load and the outer side length of the section. The calculation involves first distributing the horizontal load on a single pile evenly according to the number of piles, and then calculating it according to the bending stiffness of each pile. The final allocation value is obtained by performing a weighted iterative correction. Total displacement of the mud surface. The calculation is based on the pile group effect coefficient of mud surface displacement, elastic limit horizontal load, pile deformation coefficient, weighted pile length, weighted moment of inertia, number of straight piles, number of inclined piles, and inclined pile coefficient, among which the pile deformation coefficient is calculated. From the horizontal resistance coefficient proportional coefficient Calculate the width With the moment of inertia of the cross section according to Determined. Mud surface displacement group pile effect coefficient. By elastic limit displacement Displacement of the pile top caused by deformation of the pile body above the mud surface The difference is obtained by dividing the total displacement of the mud surface by the foundation amount, that is The values ​​were then processed and calibrated to be the initial values ​​under the complete structure. The purpose of this step is to establish a displacement calculation benchmark under the complete structural state, providing a reference for subsequent damage correction.

[0058] The specific implementation of step S3 is to obtain the damage area ratio of each damaged pile. Its value is the area of ​​damage. Divide by the total cross-sectional area The value ranges from 0 to 100%. Based on the three-zone superposition rule of the cross-section, the cross-section is divided into a compressive damage zone, a tensile cracking zone, and a neutral axis proximity zone. The damage reduction contribution of each zone to the cross-section's moment of inertia is calculated separately. Based on the superposition principle of structural mechanics, the total effective bending stiffness of the cross-section after damage is obtained. Its initial bending stiffness in the undamaged state The ratio is used as the reduction ratio. The physical basis of the three-zone superposition rule is that the contribution of each zone of the cross section to the bending stiffness varies significantly due to different stress states. The degree of contribution loss in the compressive damage zone and the tensile cracking zone differs from that in the neutral axis adjacent zone. This difference can be accurately reflected by geometric integration zone calculation. For hollow square straight piles, the cross section is divided into four rectangles on average. When the bending moment zone is completely damaged, the stiffness is reduced by about 71%, and when the shear force zone is completely damaged, the stiffness is reduced by about 29%. For inclined piles, the ratio of damaged area to stiffness reduction ratio is determined according to a 1:1 relationship. Considering that the length of the local damaged section at the pile top is much smaller than the calculated length of the pile body, this step adopts a simplified treatment method of uniform stiffness reduction for the entire pile. In this step, the mechanical conservation residual dense jump graph topology evolution model assists in the adaptive correction of the equivalent bending stiffness of the damaged section and the dynamic redistribution calculation of the multi-pile damaged stiffness field. It determines the redistribution path of internal forces among the piles through maximum flow and minimum cut iteration of graph theory network flow, ensuring the convergence and physical rationality of the multi-pile damaged stiffness evolution reconstruction. The purpose of this step is to accurately quantify the stiffness degradation of each damaged pile and construct the mapping relationship between the damaged area ratio and the structural stiffness degradation, providing input for subsequent correction of the pile group effect coefficient.

[0059] The specific implementation of step S4 is as follows: based on the equal displacement failure criterion, assuming that both the damaged pile and the intact pile fail when they reach the preset elastic limit displacement, the expression for the total displacement at the pile top under the damaged state is made equal to the expression for the displacement under the intact state, and the pile group effect coefficient of the pile top displacement under the damaged state is derived. Coefficient of effect of pile group with mud surface displacement The corrected formula. Normalized and Ratio of each to the damaged area The relationships between the piles satisfy a quadratic polynomial or linear function, and the coefficients are obtained through regression analysis of multiple sets of numerical simulation conditions. When multiple piles are damaged simultaneously, the damage effect multiplication coupling rule is used to calculate the coefficients for each individual pile damaged independently. Then, the corresponding coefficients of each individual pile are multiplied sequentially to obtain the overall pile group effect coefficient when multiple piles are damaged simultaneously. The physical basis of this coupling rule is that, under conventional pile spacing conditions, the influence of damage to each pile on the overall stiffness of the pile group can be approximated as independent, and the product result retains the independent mechanical contribution of each pile's damage. When the damage area ratio of any pile reaches 100%, the pile is considered completely destroyed, and the subsystem composed of the remaining intact piles is considered as a new complete structure. The pile group effect coefficient is then recalibrated according to step S2. The mud surface displacement pile group effect coefficient can also be determined by introducing a regression formula with an indicator variable of the number of missing piles and an interaction term on the same side to reflect the additional influence of asymmetric damage on the pile group effect. The purpose of this step is to transform the stiffness degradation information at the individual pile section level to the structural level to obtain the pile group effect coefficient that reflects the actual damage state.

[0060] The specific implementation of step S5 is to use the pile top displacement group pile effect coefficient under the damaged state. Coefficient of effect of pile group with mud surface displacement Substitute the steps described in step S2 and The calculation formula is used to calculate the total horizontal displacement of the pile top under various load levels. This process generates a load-displacement curve. The total horizontal displacement at the pile top is the sum of the displacement at the pile top caused by the deformation of the pile body above the mud surface and the displacement at the mud surface. Both parts are calculated using the group pile effect coefficient under damaged conditions, substituted into the formula framework under intact conditions, ensuring the consistency of the calculation method. The purpose of this step is to generate a complete load-displacement curve, providing a data foundation for subsequent two-way calculations.

[0061] The specific implementation of step S6 is to use the elastic limit displacement determined in step S2. As a failure criterion, a two-way calculation is performed using the load-displacement relationship curve generated in step S5. When the external horizontal load is known, the corresponding total horizontal displacement at the pile top is retrieved from the curve to assess the structural deformation safety under the current damage state. When the elastic limit displacement is known, the finite displacement of the structure under the damage condition is calculated from the curve, serving as the basis for assessing the remaining bearing capacity of the structure. This two-way calculation method makes this approach applicable to both displacement assessment under known load conditions and bearing capacity calculation based on displacement limits, demonstrating strong engineering applicability. The purpose of this step is to transform the load-displacement relationship curve into actual engineering evaluation results, completing the determination of the finite displacement under the damage state of the high-pile wharf.

[0062] It should be noted that the key technologies of this invention include: the three-zone superposition method of the cross section, which calculates and superimposes the stiffness contributions of the compressive damage zone, tensile cracking zone, and neutral axis adjacent zone of the cross section through geometric integration, overcomes the defect of the traditional uniform reduction assumption that ignores the stress differences in different regions of the cross section, and makes the mapping relationship between the damage area ratio and the stiffness reduction ratio physically differentiable. The equal displacement failure criterion establishes an analytical relationship between the damage group pile effect coefficient and the intact group pile effect coefficient by making the expression of the total displacement at the pile top in the damaged state equal to that in the intact state, so as to keep the correction amount consistent with the stiffness change, pile length change and foundation soil parameter change of the damaged pile, thereby avoiding the physical irrationality of pure statistical regression under extrapolation conditions. The damage influence multiplication coupling method decomposes the multi-pile damage problem into the product of the single-pile independent damage problem under the conventional pile spacing condition. The calculation dimension is lower than that of the full matrix coupling method, and each factor is derived from physics. The product result retains the independent mechanical contribution of each pile damage. The synergistic effect of the above three key technologies enables this method to form a complete physical link from the quantification of stiffness degradation at the single pile section level, to the correction of the pile group effect coefficient, and then to the calculation of the overall displacement of the multi-pile coupling. Compared with the traditional fixed pile group effect coefficient method, it has a clear physical basis and higher calculation accuracy in the scenario of multi-pile asymmetric damage.

[0063] It should be noted that in the case of multiple pile foundations in a high-pile wharf structure experiencing asymmetric damage of varying degrees at the same time, the stiffness degradation of each pile in the structure is different, resulting in a dynamic redistribution of the transmission path of horizontal loads among the piles, and the horizontal displacement response of the overall structure exhibits highly nonlinear characteristics.

[0064] The aforementioned technical problems arise because when multiple piles are damaged simultaneously with varying damage area ratios, the stiffness degradation of each pile differs. Piles with higher stiffness will bear more horizontal internal forces, while damaged piles with lower stiffness will bear less internal force. This redistribution of internal forces makes it impossible to directly reflect the overall structural response based solely on the results of individual pile damage analysis. Furthermore, the asymmetrical arrangement of damage causes the effective stiffness center of the pile group to shift, further increasing the complexity of overall displacement calculation.

[0065] The usual solution to the aforementioned technical problems is to establish a complete stiffness matrix for all piles, calculate the internal force coupling relationship between piles through matrix operations, and then solve for the overall displacement. However, in multi-pile asymmetric damage scenarios, the stiffness matrix dimension expands rapidly with the number of piles, and the matrix elements need to be recalculated with each change in damage state, resulting in a large computational load and unsuitability for direct engineering applications. Furthermore, the traditional fixed group pile effect coefficient method completely ignores the redistribution of internal forces caused by damage, and the systematic error accumulates with the increase of the number of damaged piles, failing to meet the calculation accuracy requirements under multi-pile asymmetric damage.

[0066] This invention effectively solves this technical problem. It derives a correction formula for the group pile effect coefficient when each individual pile is independently damaged, based on the equal displacement failure criterion. This correction formula explicitly incorporates the changes in stiffness, pile length, and foundation soil parameters of the damaged piles into the coefficient correction, with a clear physical meaning. Building upon this, the damage influence multiplication coupling law utilizes the physical assumption that the damage to each pile is independent under conventional pile spacing conditions. It expresses the overall group pile effect coefficient when multiple piles are simultaneously damaged as the product of the independent damage coefficients of each individual pile. This transforms the matrix operation, whose dimensionality increases dramatically with the number of piles, into a simple product operation of several individual pile coefficients. The computational complexity is linearly related to the number of piles rather than exponentially. Simultaneously, the mechanical conservation residual dense jump graph topology evolution model, through maximum flow and minimum cut iteration of graph theory network flow, accurately describes the internal force redistribution path under multi-pile damage at the artificial intelligence level. This ensures that the input parameters of each individual pile correction coefficient remain accurate at the physical level, thereby guaranteeing the accuracy of the multiplication coupling results. This approach, based on physical principles, ensures computational accuracy while keeping computational complexity within an acceptable range for engineering applications. It effectively overcomes the shortcomings of traditional methods that suffer from systematic deviations due to neglecting the redistribution of internal forces in multi-pile asymmetric damage scenarios.

[0067] Specifically, the principle of this invention is:

[0068] The fundamental reason why this invention can solve the above-mentioned technical problems is that it decomposes the damage effect from the structural level to the single pile section level, and then restores it to the structural level through the coupling law, forming a calculation link with complete physical meaning.

[0069] First, the three-zone superposition method of the cross-section, starting from the perspective of geometric integration, divides the cross-section into a compressive damage zone, a tensile cracking zone, and a neutral axis proximity zone. The contribution of each zone to the reduction of the cross-section's moment of inertia is calculated separately. Then, based on the superposition principle of structural mechanics, the effective flexural stiffness reduction ratio of the damaged cross-section is obtained. This approach conforms to the plane section assumption and the definition of flexural stiffness integral in mechanics of materials, making the functional relationship between the reduction ratio and the damage area ratio physically differentiable, rather than empirically fitted, thus ensuring the accuracy of quantifying the stiffness degradation of a single pile.

[0070] Secondly, the introduction of the equal displacement failure criterion provides a mechanical constraint for correcting the pile group effect coefficient under damaged conditions. This criterion assumes that damaged piles and intact piles fail when they reach the same elastic limit displacement. By making the expressions for the total displacement at the pile top equal in both damaged and intact states, the analytical relationship between the damaged pile group effect coefficient and the intact pile group effect coefficient is directly derived. This derivation process ensures consistency between the coefficient correction amount and the changes in stiffness, pile length, and foundation soil parameters of the damaged pile, avoiding the physical irrationality of pure statistical regression methods under extrapolation conditions.

[0071] Furthermore, the damage-effect multiplication coupling method decomposes the multi-pile damage problem into a product of multiple independent single-pile damage problems. This is based on the fact that, under conventional pile spacing conditions, the impact of damage to each pile on the overall stiffness of the pile group can be approximated as independent, and the product of the damage correction coefficients of each individual pile is equivalent to the overall correction coefficient when multiple piles are damaged simultaneously. This approach significantly reduces the computational dimensionality compared to the full matrix coupling method. Simultaneously, because the coefficients of each individual pile are derived from physics, the product result retains the independent mechanical contribution of each pile's damage, making displacement calculations under multi-pile asymmetric damage conditions both physically grounded and easily applicable in engineering.

[0072] Finally, the mechanical conservation residual dense jump graph topology evolution model embeds the above physical constraints into the loss function and hidden layer operators of the artificial intelligence network. It dynamically describes the internal force redistribution path under multi-pile damage through the maximum flow and minimum cut iteration of graph theory network flow. This allows the model to still satisfy the internal force balance constraint when generalizing to the case where no damage is observed. It fundamentally overcomes the defect that the traditional fixed path assumption cannot reflect the phenomenon of internal force flow around damage, and ensures the convergence and physical rationality of the damage stiffness evolution reconstruction.

[0073] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0074] Specific implementation of step S1: Collect the structural geometric parameters of the high-pile wharf, including the inclination angle of the inclined piles. Moment of inertia of cross section Elastic modulus Cross-sectional area , outer side length of cross section and the inner side length of the cross section and the length of the free section of each pile .in The value range is determined based on the wharf design documents, with a typical value of 15° to 30°. The typical value is The typical value for straight piles is 0.45–0.65m, and for inclined piles it is 0.40–0.60m. The typical value for straight piles is 0.25–0.35m, and for inclined piles it is 0.22–0.32m. Due to variations in the undulating slope topography, measurements must be taken on a pile-by-pile basis to determine the exact values. Simultaneously, the proportional coefficient of the horizontal resistance coefficient of the foundation soil along the pile should be collected. Property conversion factor and the influence coefficient of the pile ,in Based on vane shear strength Calculate using the following formula:

[0075] ;

[0076] In the formula, Shear strength of the vane, in units of The results were obtained through on-site vane shear tests, layer by layer. Units are This reflects the rate of change of the horizontal resistance of the soil along the pile as the depth increases. and The weighted calculation was obtained according to the port engineering pile foundation specifications. A conversion factor to reflect differences in soil properties. This is a coefficient that reflects the effect of pile diameter.

[0077] Specific implementation of step S2: Determine the pile top displacement group pile effect coefficient under the condition of complete piles. Coefficient of effect of pile group with mud surface displacement Initial value. The empirical value is 1.0, with a range of 0.8 to 1.2, adjusted within this range based on pile spacing, number of piles, and pile arrangement. Elastic limit displacement. Take the outer side length of the cross section 0.8 times:

[0078] ;

[0079] In the formula, This represents the structural elastic limit displacement. The length of the outer side of the cross-section is determined based on the statistical results of numerical simulation of the hollow square pile high-pile wharf. The formula for calculating the pile length is as follows: ,in The length of the free section of the pile body. The embedding point depth is calculated using the following formula:

[0080] ;

[0081] In the formula, The horizontal load borne by a single pile is expressed in units of 1. First, distribute the load evenly according to the number of piles, then distribute it according to the bending stiffness of each pile. The final allocation value is obtained by performing a weighted iterative correction. Units are In the formula, coefficients 6 and 0.016 are empirical coefficients based on standard statistics, with the unit of 0.016 being... To ensure dimensional consistency. The displacement of the pile top caused by pile deformation above the mud surface. The calculation formula is:

[0082] ;

[0083] In the formula, This is the coefficient for the pile top displacement group pile effect. The elastic limit horizontal load is expressed in units of... Obtained from numerical simulation statistics For elastic modulus, Let the moment of inertia of the cross section be... The inclination angle of the inclined pile. For the number of straight piles, For the number of inclined piles, Calculate the pile length for the pile body. The numerator is the cross-sectional area; the numerator of this formula is the modified elastic limit load, and the denominator is the combined lateral stiffness of the pile group. The ratio of the two is the pile top displacement. Total displacement of the mud surface. The calculation formula is:

[0084] ;

[0085] In the formula, The coefficient for the mud surface displacement group pile effect is given. Weighted pile length for all piles, in units of Weighted moment of inertia for all piles, in units of This is the pile deformation coefficient, in units of... The calculation formula is:

[0086] ;

[0087] In the formula, To calculate the width-weighted value, the unit is... The calculation formula is:

[0088] ;

[0089] In the formula, The force conversion factor is calculated using the following formula:

[0090] ;

[0091] In the formula, The coefficient is dimensionless. middle Units are The coefficient 1 of this term has a unit of 1. To ensure Dimensionless The weighted value of the inclined pile coefficient is calculated using the following formula:

[0092] ;

[0093] In the formula, This is a dimensionless coefficient, reflecting the reduction effect of the lateral stiffness contribution of inclined piles compared to straight piles. In the formula, the numerator contains a combination of pile group effect correction, elastic limit load and weighted pile length, and the denominator is the product of the comprehensive equivalent stiffness of the pile group and the deformation coefficient. The ratio of the two gives the horizontal displacement of the mud surface. The calibration formula is:

[0094] ;

[0095] In the formula, the numerator is the difference between the elastic limit displacement and the pile top deformation displacement, which is the target value of the mud surface displacement; the denominator is the calculated value of the mud surface displacement corresponding to the unit group pile effect coefficient; the ratio of the two is the group pile effect coefficient required to make the mud surface displacement match the target value, which is calibrated by the corresponding load when simulating the elastic limit displacement numerically.

[0096] Specific implementation of step S3: Damage area ratio Defined as:

[0097] ;

[0098] In the formula, The area of ​​damage is expressed in units of... The total cross-sectional area is expressed in units of 1000g. This is a dimensionless ratio, ranging from 0% to 100%. The effective flexural stiffness reduction ratio of the damaged pile section is calculated using a three-zone superposition method. The section is divided into a compressive damage zone, a tensile cracking zone, and a neutral axis proximity zone. The damage reduction contribution of each zone to the section's moment of inertia is calculated separately, and the total effective flexural stiffness of the damaged section is obtained by combining these factors. Initial bending stiffness in the undamaged state The ratio, i.e., the stiffness reduction ratio :

[0099] ;

[0100] In the formula, This is a dimensionless stiffness reduction ratio. To ensure the effective bending stiffness of the cross section after damage, The initial bending stiffness is the value under undamaged conditions. For hollow square straight piles, the stiffness is reduced by approximately 71% when the bending moment zone is completely damaged, and by approximately 29% when the shear force zone is completely damaged. For inclined piles, the ratio of damaged area to stiffness reduction is 1:1. The mechanical conservation residual dense jump graph topology evolution model assists in the reconstruction of multi-pile damaged stiffness evolution in this step, inputting the equivalent bending stiffness reduction rate of the damaged section and outputting the updated moment of inertia of the damaged pile section. Compared with elastic limit horizontal load .

[0101] The specific implementation method of step S4: Derive the pile top displacement group pile effect coefficient under damage state based on the equal displacement failure criterion. Coefficient of effect of pile group with mud surface displacement , The corrected formula is:

[0102] ;

[0103] In the formula, The moment of inertia of the damaged pile section, in units of The output is from the topological evolution model of the mechanical conservation residual dense jump graph in step S3. The unit is the elastic limit horizontal load for numerical simulation of displacement failure of the damaged pile, in units of The output of this model Calculate the pile length for damaged piles, in units of The parameters are recalculated based on the damage condition. The numerator of this formula represents the lateral stiffness under damage conditions, and the denominator represents the lateral stiffness under intact conditions. The ratio of the two reflects the degree of stiffness degradation caused by damage, which is then combined with the load ratio. For the complete state Perform dynamic corrections. The corrected formula is:

[0104] ;

[0105] In the formula, This is the proportionality coefficient of the horizontal resistance coefficient of the foundation soil along the pile side corresponding to the length of the damaged pile, in units of... Re-measure the length of the pile after the damage. The coefficient for pile inclination due to damage is dimensionless and recalculated based on the parameters after damage. The ratios in this formula reflect the effects of changes in pile length, degradation of moment of inertia, changes in the effective number of piles in a group, and changes in soil resistance coefficient on mud surface displacement, respectively. The power originates from the pile deformation coefficient. The definition of the fifth root. After normalization. and The functional relationship between them, for both straight piles and bearing-pressure inclined piles, is as follows:

[0106] ;

[0107] For tension-bearing inclined piles:

[0108] ;

[0109] and The functional relationship between them, for straight piles, is as follows:

[0110] ;

[0111] For inclined piles:

[0112] ;

[0113] The coefficients in the above four regression formulas were obtained through regression analysis of multiple sets of numerical simulation working conditions. All quantities in the formulas are dimensionless. When multiple piles are damaged simultaneously, the calculation formula for the multiplicative coupling law of damage effects is as follows:

[0114] ;

[0115] ;

[0116] In the formula, and The first Correction coefficients for pile top displacement and mud surface displacement under independent pile damage: The total number of damaged piles, and This represents the overall pile group effect coefficient when multiple piles are damaged simultaneously. When any one pile... When the percentage reaches 100%, the group pile effect coefficient is recalibrated according to step S2 using the remaining intact piles as the subsystem.

[0117] Specific implementation of step S5: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] and Substituting into the formula described in step S2, calculate the total horizontal displacement of the pile top under each load level:

[0118] ;

[0119] In the formula, This represents the total horizontal displacement at the pile top, in units of... and All with and Replace each and Substitute the values ​​into the corresponding formula in step S2 to calculate, and then generate the load-displacement relationship curve.

[0120] Specific implementation of step S6: using elastic limit displacement As a failure criterion, a two-way calculation is performed using the load-displacement relationship curve. This is based on a given horizontal load. Find the total horizontal displacement of the corresponding pile top Or by elastic limit displacement Inverse calculation of finite displacement of structure under damage conditions, inverse calculation time... Solve for the corresponding load level to determine the ultimate bearing capacity of the structure under damage conditions.

[0121] Specific implementation of the mechanical conservation residual dense jump graph topology evolution model: This model abstracts the spatial structure of the high-pile wharf into a weighted directed graph. ,in It is a set of nodes (including pile top nodes and mud surface nodes). Let be a set of directed edges. This is a set of edge weights, where each edge weight represents the reduced flexural stiffness of the corresponding pile. In the pre-processing stage, the input sensor stream data is used to construct a third-order tensor. ,in Geometric dimensions For load dimensions, The dimension of the damage state is defined; after orthogonal decoupling using a third-order tensor, singular value decomposition is performed along the three orthogonal dimensions to obtain the decoupled orthogonal feature matrix. The decomposition formula is as follows:

[0122] ;

[0123] In the formula, For the third-order tensor along the first The expansion matrix of the dimension, It is a left singular vector matrix. It is a singular value diagonal matrix. The transpose of the right singular vector matrix, with subscripts... Pick , , These correspond to three dimensions: geometry, load, and damage state. Each dimension is decomposed independently, achieving decoupling of information between dimensions and ensuring that the hidden layer features of each dimension do not interfere with each other. The hidden layer employs physical constraint operators, embedding the differential equation of pile bending deformation into the network as residual terms. Defined as:

[0124] ;

[0125] In the formula, For the pile body at depth The predicted horizontal displacement at the location is in units of For calculating the depth of the pile, the unit is . This is the pile deformation coefficient, in units of... The residuals are due to the conservation of mechanics, and the unit is . When the model prediction satisfies the differential equation for pile bending, Approaching zero ensures that physical constraints are met. Comprehensive routing index. The calculation formula is:

[0126] ;

[0127] In the formula, The maximum flow value across the entire graph at the current iteration step reflects the maximum capacity for internal force transmission within the structure. The minimum cut value in the entire diagram reflects the bearing capacity of the weakest section, indicating the transmission of internal forces within the structure. The mean of the internal force equilibrium residuals is dimensionless. To prevent extremely small positive numbers from being zero, the value is usually taken as [value missing]. This is a dimensionless comprehensive routing index that comprehensively reflects the stiffness distribution and internal force balance state of the current iteration step, used to drive branch selection in gated routing. Gated routing is based on... Perform conditional redirection: when At this time, the gated routing weights are tilted towards bypass jump paths, increasing the transmission ratio of residual jump connections to improve the model's sensitivity to low-stiffness damaged paths; when At that time, the normal path and the redirect path are each allocated in a 50% ratio; when When the gating route weights are tilted towards the main path, the bypass hop ratio is reduced to suppress excessive characteristic disturbances under high-stiffness paths; when When this occurs, the hidden layer's dynamic backtracking mechanism is triggered, forcibly correcting the stiffness matrix weights in reverse and resetting them. To prevent the model from getting trapped in local extrema under extreme load conditions, the thresholds of 0.6, 1.2, and 2.0 were statistically determined on the validation set through multiple rounds of ablation experiments. Long-span residual dense jump matrix. Define the weights of the jump connections between each layer, and the feature aggregation formula is as follows:

[0128] ;

[0129] In the formula, For the first The output feature vector of the hidden layer, For the first The regular transfer feature vector of the layer, For the first Hidden layer feature vectors of the layer For the first Layer to the first Layer jump connection weight scalar, Let be the total number of network layers. This formula weights and converges all features from upper layers to the current layer, allowing deep displacement features to directly obtain gradient information from shallow internal force features, effectively alleviating the gradient vanishing problem in deep networks. The physical constraint loss function is:

[0130] ;

[0131] In the formula, For the total loss function, For data fitting terms, For the residual terms of the differential equation of pile bending, This is the weighting coefficient, initially set to 1, and gradually increased to 3 with each training epoch to ensure the model converges while adhering to the laws of conservation of mechanics. (Graph node imbalance) Defined as:

[0132] ;

[0133] In the formula, For nodes The inflow of internal force, For nodes The outflow of internal energy For nodes Total flow As a dimensionless quantity, each iteration is based on Update the routing weights in the hidden layer of the neural network to encourage feature flow to shift towards higher stiffness paths; when A larger value indicates an internal force imbalance at the node. The algorithm will increase the transfer weight to the adjacent high-stiffness edge until iterative convergence. The model training dataset uses different pile type parameters, different combinations of free segment lengths of the bank slope, different damage area ratios, and different horizontal load conditions as the parameter space. It is generated in batches using finite element numerical simulation software and divided into training, validation, and test sets in a ratio of 7:1.5:1.5; the labels are for the corresponding load conditions. , And the key node values ​​of the load-displacement relationship curve. The optimizer uses an adaptive moment estimation algorithm with an initial learning rate of The validation set loss decays to a certain value using a cosine annealing strategy. Training stops when the validation set loss does not decrease for 20 consecutive rounds, and the weights corresponding to the optimal validation set loss are used as the final model parameters. The final model output... and , which serves as the input parameter for the coefficient correction formula in step S4.

[0134] To better understand and implement this invention, the following is a specific application scenario of this invention, Example 2:

[0135] This embodiment takes a typical high-pile wharf as an example and uses numerical simulation data to verify the calculation process and results of the horizontal displacement of the pile top under the condition of pile damage.

[0136] Obtain complete structural parameters and geometric information of the high-pile wharf. Based on... Figure 2 Taking the case where only pile No. 5 is damaged by 50% as an example, the numerical simulation results give the value of an intact pile in this case. When pile No. 5 is 50% damaged, the corresponding Inclination angle of inclined pile And when twisted about the axis at 45°, the elastic modulus The piles are hollow concrete square piles. The outer side length of the straight pile section is 0.55 m, the outer side length of the inclined pile section is 0.5 m, the inner side length of the straight pile section is 0.3 m, and the inner side length of the inclined pile section is 0.27 m. Due to the influence of the bank slope height, the free section length of pile No. 1 is... Length of free section of pile No. 2 Length of free section of pile No. 3 Length of free section of pile No. 4 Length of free section of pile No. 5 Length of free section of pile No. 6 Length of free section of pile No. 7 Length of the free section of pile No. 8 Length of the free section of pile No. 9 Length of the free section of pile No. 10 .

[0137] Determine the initial reference values ​​for the group pile effect coefficient under complete conditions. This includes the group pile effect coefficients for the pile top displacements of straight and inclined piles. Set to a preset value range, mud surface displacement group pile effect coefficient Based on the elastic limit displacement of the intact structure Corresponding elastic limit horizontal load The proportional relationship below is used for calibration. The pile top displacement caused by pile deformation above the mud surface. It can be expressed by the following formula:

[0138] ;

[0139] In the formula, For the number of straight piles, This refers to the number of inclined piles. The horizontal load borne by a single pile. First, distribute the load evenly according to the number of piles, then distribute it according to the bending stiffness of each pile. The weighted average is then iteratively corrected to obtain the final single pile load distribution value. Calculate the pile length for the pile body. The embedment depth, i.e., the distance from the point of maximum bending moment to the soil surface, is expressed by the following formula:

[0140]

[0141] Total displacement of mud surface It can be expressed by the following formula:

[0142] ;

[0143] ;

[0144] In the formula, The pile deformation coefficient The horizontal resistance coefficient of the foundation soil along the pile increases with depth, based on the vane shear strength. calculate, To calculate the width, a weighted value is used during the calculation for straight piles. Inclined pile For force conversion factors, in this working condition, straight piles Inclined pile Property conversion factor in this working condition Influence coefficient of pile This is the coefficient for inclined piles, calculated using a weighted average. In this working condition, the inclined piles... The weighted pile length for all piles, corresponding to the complete pile in this working case. When pile No. 5 is 50% damaged, the corresponding Weighted moments of inertia for all piles, corresponding to the complete pile in this working case. When pile No. 5 is 50% damaged, the corresponding .

[0145] Based on the statistical results of numerical simulation of typical high-pile wharf pile group layout, the pile top pile group effect coefficient under the complete structure is determined. The fluctuation range is 0.8–1.2, with a baseline value of 1.0. The ultimate displacement is the limit of the elastic stage. Based on the statistical results of numerical simulation of a typical high-pile wharf pile group arrangement, the elastic ultimate displacement is... for Mud-surface pile group effect coefficient The calibration is performed using the load results from numerical simulation of the elastic limit displacement, as shown in the following formula:

[0146] ;

[0147] according to Figure 2 Working conditions, mud-faced pile group effect coefficient It can be determined by the following formula:

[0148] ;

[0149] In the formula, The missing numbers for stakes 1 and 6. The missing numbers for stakes 2 and 7. The missing numbers for stakes 3 and 8. The missing numbers for stakes 4 and 9. Missing numbers for stakes 5 and 10 To determine if the other inclined pile between piles 4 and 9 is missing, if both pile 4 and 9 are missing, this item is set to 1; otherwise, it is set to 0. Check if the other inclined pile between piles 5 and 10 is missing. If both pile 5 and pile 10 are missing, this item is 1; otherwise, it is 0. For same-side interaction terms, it indicates the additional effect when the front row of diagonal piles 4 and 5 are missing simultaneously or the back row of piles 9 and 10 are missing simultaneously.

[0150] Obtain damage information of the pile foundation, based on the moment of inertia of the pile foundation section under the damage condition. With bending stiffness The reduction ratio is used to construct the damage area ratio under the damage condition. Mapping relationship between structural stiffness degradation and damage area ratio. The method for determining the damage area is... Divide by the total cross-sectional area The value ranges from 0 to 100%. In this working condition, the complete pile corresponds to... When pile No. 5 is 50% damaged, the corresponding .like Figure 3 As shown, considering that the length of the locally damaged section at the pile top is much smaller than the total pile length in the project, this method adopts a simplified approach of uniformly reducing the stiffness of the entire pile. The moment of inertia of the pile foundation section under damage conditions... With bending stiffness The reduction ratio is determined by dividing the cross-section into a compressive damage zone, a tensile cracking zone, and a neutral axis proximity zone, and calculating the damage reduction contribution of each zone to the cross-section's moment of inertia. Based on the superposition principle of structural mechanics, the total effective bending stiffness of the cross-section after damage is obtained by combining the contributions of each zone. And its initial bending stiffness in the undamaged state. The ratio is used as the reduction ratio. According to... Figure 2 Under the working condition, the straight pile is divided into four rectangular sections. When the hollow straight pile is completely damaged in the bending moment zone, its stiffness is reduced by approximately 71%, and when it is completely damaged in the shear force zone, its stiffness is reduced by approximately 29%. The ratio of the damaged area of ​​each part of the inclined pile is... The stiffness reduction ratio is 1:1.

[0151] Based on the pile foundation damage area ratio, the pile group effect coefficient in the intact state is dynamically corrected to obtain the pile group effect coefficient in the damaged state. and The group pile effect coefficient under damaged conditions satisfies a functional relationship with the ratio of damaged areas. Based on the equal displacement failure criterion, assuming that both damaged and intact piles fail when they reach a preset critical horizontal displacement, the expression for the total pile top displacement under damaged conditions is equal to the expression for the displacement under intact conditions. The group pile effect coefficient with damaged piles is expressed by the following formula:

[0152] ;

[0153] ;

[0154] In the formula, Moment of inertia of damaged pile section Numerical simulation results for displacement failure of damaged piles. For damaged pile length The proportionality coefficient of the horizontal resistance coefficient of the foundation soil along the pile side, corresponding to the pile length of the damaged pile, as it increases with depth. This is the coefficient for inclined piles damaged by the pile.

[0155] according to Figure 2 Working condition, normalized group pile effect coefficient and Ratio of damage area The following formula can be used to calculate the relationship between straight piles and bearing piles:

[0156] ;

[0157] For tension piles:

[0158] ;

[0159] For straight piles:

[0160] ;

[0161] For inclined piles:

[0162] ;

[0163] When multiple piles of a high-pile wharf are damaged simultaneously, the overall damage group pile effect coefficient is calculated using a coupling rule of multiplying damage effects. The coefficients for individual pile damage are calculated separately, and then multiplied to obtain the overall group pile effect coefficient when multiple piles are damaged simultaneously. According to... Figure 2 Based on the working conditions and numerical simulation results, when pile No. 5 and pile No. 8 both suffer 50% damage, the normalized group pile effect coefficient is... and The values ​​are 0.892520926 and 0.938453409, respectively; when pile No. 5 suffers 25% damage alone, the normalized group pile effect coefficients are... and The values ​​are 0.936493148 and 0.967724977, respectively; when pile No. 8 suffers 25% damage alone, the normalized group pile effect coefficients are... and The values ​​are 0.950072156 and 0.967382845, respectively. Based on some specific numerical simulation conditions in this embodiment, the coupling rule of multiplying damage effects was used for calculation. The results are shown in Table 1, and the relative error is less than 1%, proving that the rule has extremely high fitting accuracy under this condition.

[0164] Table 1 Comparison of calculation results using the coupling rule

[0165]

[0166] As shown in Table 1, with the increase of the number of damaged piles, the absolute value of the error between the calculated value and the numerical simulation value of the coupling rule remains at a low level. This trend indicates that the multiplicative coupling rule of damage effects can effectively suppress the accumulation of systematic errors caused by asymmetric damage of multiple piles under the physical assumption that the damage of each pile is independent. This solves the technical defect of the traditional fixed pile group effect coefficient method in the multi-pile damage scenario due to neglecting the redistribution of internal forces.

[0167] When the damaged area of ​​any one pile is greater than When the number of piles reaches 100%, the pile is considered to be completely destroyed and no longer contributes to the overall stiffness of the structure. At this point, the subsystem consisting of the remaining intact piles is regarded as a new complete structure, and the pile group effect coefficient under the undamaged state is recalibrated according to the method in step S2.

[0168] The coefficient of the pile group effect under the damaged state and Substitute the pile top displacement caused by pile deformation above the mud surface Total displacement of mud surface The calculation formula yields the total horizontal displacement at the pile top after pile damage under a given horizontal load. The total horizontal displacement at the pile top is the displacement at the pile top caused by the deformation of the pile body above the mud surface. Displacement at mud surface The sum is expressed by the following formula:

[0169]

[0170] According to the established and Substituting the values ​​into the displacement calculation formula, the displacement values ​​under different load levels are calculated. The calculation results for this working condition are as follows: Figure 4 As shown.

[0171] The load-displacement curve obtained from the calculation can be used for bidirectional calculation: with a set elastic limit displacement. As a failure criterion, the finite displacement of the structure under the damage condition can be calculated from the curve; if the externally applied horizontal load is known, the pile top displacement value under the corresponding damage state can also be quickly obtained from the curve to assess the structural deformation safety. Figure 4 As shown, the displacement-load correspondence under different horizontal loads can be obtained under this damage condition. When the horizontal load is 1000 kN, the total horizontal displacement at the top of the intact pile in this condition is... The total horizontal displacement of the pile top when pile No. 5 is 50% damaged .Depend on Figure 4It is evident that as the damage area ratio increases, the load-displacement curve under the damaged condition gradually deviates from the curve under the intact condition, and the displacement value tends to increase under the same load level. This reflects the physical essence of the reduction in the effective bending stiffness of the section leading to a decrease in the overall horizontal stiffness of the structure. This is consistent with the macroscopic manifestation of the difference in stiffness contribution of each section at the structural level described by the three-section superposition rule. From a physical mechanism perspective, this verifies the rationality of the method for calculating the horizontal displacement under the asymmetric damage condition of multiple piles.

[0172] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining the finite displacement of a high-pile wharf structure with pile damage under horizontal loading conditions, characterized in that, Includes the following steps: Collect structural geometric parameters and soil parameters of the pile-side foundation of the high-pile wharf; Determine the initial values ​​of the pile top displacement group pile effect coefficient and the mud surface displacement group pile effect coefficient under the complete pile state. The pile top displacement group pile effect coefficient is taken within the preset range, and the mud surface displacement group pile effect coefficient is calibrated based on the proportional relationship between the elastic limit horizontal load and the elastic limit displacement. The damage area ratio of each damaged pile is obtained. Based on the three-part superposition rule of the cross-section compression damage zone, tension cracking zone and neutral axis adjacent zone, the effective bending stiffness reduction ratio of the damaged pile cross-section is calculated. The mapping relationship between the damage area ratio and the structural stiffness degradation is constructed. The topological evolution model of the mechanical conservation residual dense jump graph is used to assist in the reconstruction of the multi-pile damage stiffness evolution. The pile top displacement group pile effect coefficient and mud surface displacement group pile effect coefficient are dynamically corrected based on the damage area ratio. When multiple piles are damaged at the same time, the damage influence multiplication coupling law is used to calculate the overall damage group pile effect coefficient. When the damage area ratio reaches the complete damage threshold, the group pile effect coefficient of the subsystem composed of the remaining intact piles is recalibrated. Substitute the pile top displacement group pile effect coefficient and mud surface displacement group pile effect coefficient under the damaged state into the pile top displacement formula to calculate the total horizontal displacement of the pile top under each load level and form a load-displacement relationship curve. Using the elastic limit displacement as the failure criterion, and combining the load-displacement relationship curve, a two-way calculation is performed. The total horizontal displacement at the top of the pile can be obtained from the given horizontal load, or the finite displacement of the structure under the damage condition can be calculated from the elastic limit displacement.

2. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 1, characterized in that, The structural geometric parameters specifically include the inclination angle of the inclined pile, the moment of inertia of the cross section, the elastic modulus, the cross-sectional area, the outer side length of the cross section, the inner side length of the cross section, and the length of the free segment of each pile; the pile side foundation soil parameters specifically include the horizontal resistance coefficient proportionality coefficient, the property conversion coefficient, and the pile influence coefficient.

3. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 2, characterized in that, The pile top displacement caused by the deformation of the pile body above the mud surface is specifically calculated using the pile top displacement group pile effect coefficient, elastic limit horizontal load, section moment of inertia, elastic modulus, inclined pile inclination angle, number of straight piles, number of inclined piles, and calculated pile length. The calculated pile length is determined by the sum of the free section length and the embedment point depth, and the embedment point depth is determined by the product of the single pile horizontal load and the outer side length of the section. The single pile horizontal load is first evenly distributed according to the number of piles, and then iteratively corrected according to the bending stiffness of each pile to obtain the final distribution value.

4. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 3, characterized in that, The total displacement of the mud surface is specifically calculated using the mud surface displacement group pile effect coefficient, elastic limit horizontal load, pile deformation coefficient, weighted pile length, weighted moment of inertia, number of straight piles, number of inclined piles, and inclined pile coefficient. The pile deformation coefficient is determined by the horizontal resistance coefficient proportionality coefficient, calculated width, and cross-sectional moment of inertia. The inclined pile coefficient is determined by the inclined pile inclination angle, cross-sectional moment of inertia, cross-sectional area, and calculated pile length.

5. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 4, characterized in that, The calibration of the mud surface displacement group pile effect coefficient is specifically obtained by dividing the difference between the elastic limit displacement and the pile top displacement caused by the deformation of the pile body above the mud surface by the total mud surface displacement.

6. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 5, characterized in that, The three-zone superposition rule specifically divides the cross section into a compressive damage zone, a tensile cracking zone, and a neutral axis proximity zone. The damage reduction contribution of each zone to the cross section's moment of inertia is calculated separately. Based on the superposition principle of structural mechanics, the total effective bending stiffness of the damaged cross section is obtained, and its ratio to the initial bending stiffness in the undamaged state is used as the reduction ratio. For hollow square piles, the stiffness reduction reference value is 71% when the bending moment zone is completely damaged, and 29% when the shear force zone is completely damaged. For inclined piles, the damage area ratio and stiffness reduction ratio are determined in a one-to-one relationship.

7. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 6, characterized in that, The mechanical conservation residual dense jump graph topology evolution model specifically abstracts the high-pile wharf structure into a weighted directed graph, where nodes represent pile top nodes and mud surface nodes, and directed edge weights represent the reduced bending stiffness of the foundation piles; the hidden layer adopts a physical constraint operator constructed based on the differential equation of pile bending deformation, and the feature transmission path is dynamically determined by gating routing based on the internal force balance residual at the nodes. An internal long-span residual dense jump matrix is ​​constructed to splice shallow internal force features and deep displacement features in the channel dimension; when the internal force balance error exceeds the adaptive threshold, the hidden layer dynamic backtracking mechanism is triggered to correct the stiffness matrix weights in reverse.

8. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 7, characterized in that, The mechanical conservation residual dense jump graph topology evolution model is embedded with a multi-pile damage stiffness evolution reconstruction algorithm based on graph theory network flow. Specifically, the equivalent bending stiffness reduction rate of the damaged section is used as the upper limit of the network flow capacity. The redistribution path of internal forces among the piles is determined by calculating the maximum flow and minimum cut of the whole graph. The routing selection weights of the hidden layer of the neural network are updated according to the unbalance of the graph nodes. The neuron connection strength is updated in real time in each iteration to ensure the convergence of stiffness evolution.

9. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 8, characterized in that, The mechanical conservation residual dense jump graph topology evolution model sets a stiffness routing allocation function, which calculates the comprehensive routing index based on the maximum flow value, the minimum cut value, and the mean value of the internal force balance residuals of the entire graph. The gating routing weights are dynamically adjusted based on the comparison results of the comprehensive routing index with the low stiffness threshold, the lower limit threshold of medium stiffness, the upper limit threshold of medium stiffness, and the high stiffness threshold.

10. The method for determining the finite displacement of a high-pile wharf structure under horizontal loading conditions according to claim 9, characterized in that, The dynamic correction specifically involves, based on the equal displacement failure criterion, setting the expression for the total displacement at the pile top under damaged conditions to be equal to the expression for the displacement under intact conditions. This leads to the derivation of correction formulas for the pile top displacement group effect coefficient and the mud surface displacement group effect coefficient under damaged conditions, relating to the moment of inertia of the damaged pile section, the elastic limit horizontal load of the damaged pile, the pile length of the damaged pile, the proportional coefficient of the horizontal resistance coefficient of the foundation soil of the damaged pile, and the inclined pile coefficient of the damaged pile. The coefficients of these correction formulas are obtained through regression analysis of multiple sets of numerical simulation working conditions.

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