A Fast Prediction Method for Consolidation Settlement of Horizontal Vacuum Preloaded Soft Soil Based on Operator Learning

Abstract

This invention relates to the field of foundation treatment in geotechnical engineering, and particularly to a rapid prediction method for consolidation settlement of horizontally vacuum preloaded soft soil based on operator learning. The method includes the following steps: S1. Constructing a multidimensional consolidation control parameter space; S2. Establishing nonlinear large-strain consolidation control equations and performing batch high-fidelity solutions; S3. Constructing a unified format dataset required for operator learning; S4. Constructing and training a DeepONet operator model; S5. Validating and deploying the operator model; S6. Achieving real-time prediction of the entire consolidation process and its engineering application. The surrogate model generated by this invention can predict complex nonlinear large-strain consolidation responses at millisecond speeds and can be used for construction design optimization and evaluation of resource utilization after soft soil consolidation. This invention achieves real-time solution of the two-dimensional nonlinear large-strain consolidation equations, breaking through the computational efficiency bottleneck of traditional numerical methods, and has significant engineering application value.

Description

Technical Field

[0001] This invention relates to the field of foundation treatment in geotechnical engineering, and in particular to a rapid prediction method for consolidation settlement of horizontal vacuum preloading soft soil based on operator learning. Background Technology

[0002] River dredging, lake clearing, and port and waterway construction inevitably generate large amounts of dredged silt and soft soil. Resource utilization is the fundamental solution for disposing of dredged silt and soft soil. Due to the poor physical and mechanical properties of dredged silt and soft soil (such as high water content, high compressibility, low strength, and low bearing capacity), dewatering and reinforcement treatment is often required before resource utilization (including as fill material in roadbed and embankment projects). Given limitations in treatment costs, equipment, and scale, on-site stockpiling remains the primary method in practice. However, under natural conditions, the self-weight consolidation of soft soil stockpiles often takes a long time, is greatly affected by external climate, and results in long site turnover times. Therefore, engineering projects require treatment of soft soil stockpiles to achieve rapid and effective dewatering.

[0003] The commonly used method is to install Prefabricated Vertical Drains (PVD) to provide drainage channels. However, the main problems are: PVD bends and deforms as the soil settles, resulting in poor drainage efficiency in the later stages; the dredged silt and soft soil at the bottom cannot be dehydrated and consolidated; and the early strength of the dredged silt and soft soil is low, making it difficult to implement mechanical construction of PVD.

[0004] To address the shortcomings of PVD, scholars have proposed using horizontal drainage boards (PHD) to treat dredged silt and soft soil dumps.

[0005] Compared to the vertical drainage board vacuum preloading method, the horizontal drainage board vacuum preloading method effectively avoids the twisting and bending problems caused by the large deformation consolidation settlement of high water content soft soil because the drainage boards are laid horizontally with their length extending perpendicular to the direction of soft soil settlement. Furthermore, field test monitoring results show that the vacuum load does not significantly decrease along the length of the drainage board (PHD). Since the PHD can be laid layer by layer, simultaneous backfilling and reinforcement can be achieved, significantly improving treatment efficiency. Compared to the vertical drainage board vacuum preloading method, the horizontal drainage board vacuum preloading method has inherent advantages in treating high water content dredged silt and soft soil. However, current research on the horizontal drainage board vacuum preloading method is still in the exploratory stage, especially in terms of related theoretical research, which lags far behind. A deep understanding of its mechanism of action is lacking, and relevant calculation theories are severely deficient, seriously hindering the widespread application of this method.

[0006] From the perspective of basic soil mechanics principles, PHD treatment of dredged silt and soft soil essentially adds a drainage boundary within a single soil layer, and the fundamental equations governing this consolidation process can still be derived based on Terzaghi's theory. However, the high compressibility of dredged silt and soft soil leads to large strain and nonlinear characteristics during its consolidation deformation process, which makes solving the fundamental consolidation equations exceptionally complex.

[0007] Traditional methods for solving the consolidation equations of dredged silt and soft soil mainly fall into two categories: analytical methods and numerical methods. While analytical methods can yield solutions with a certain degree of accuracy under specific conditions, their derivation is complex and typically only applicable to situations with simple soil properties and ideal boundary conditions. These methods often rely on approximate assumptions, such as neglecting nonlinearity and large strain characteristics under the assumption of regional seepage, thus simplifying the PHD two-dimensional consolidation control equations and limiting their applicability in complex practical engineering projects. In contrast, numerical methods (such as the finite difference method and the finite element method) have a wider range of applications and can handle more complex soil constitutive models and boundary conditions. However, numerical methods also have significant drawbacks, such as high computational costs and the need for re-meshing when soil parameters or boundary conditions change, making real-time equation solving difficult. This limitation prevents real-time prediction of the settlement process of soft soil layers, thus hindering the provision of timely and efficient technical support for the dynamic optimization of foundation treatment construction schemes.

[0008] In summary, existing methods still have significant shortcomings in terms of computational efficiency, accuracy, and predictive ability, and there is an urgent need to develop a new solution strategy to overcome the current technical bottlenecks. Summary of the Invention

[0009] This invention provides a rapid prediction method for consolidation settlement of horizontal vacuum preloading soft soil based on operator learning, aiming to solve the problems of highly nonlinear consolidation process, significant large strain characteristics, long time consumption of traditional numerical calculation and difficulty in real-time prediction in the treatment of dredged silt and soft soil by horizontal drainage board vacuum preloading.

[0010] This invention provides a rapid prediction method for consolidation settlement of horizontally vacuum preloaded soft soil based on operator learning, comprising the following steps:

[0011] S1. Construct a multidimensional consolidation control parameter space: Using vacuum negative pressure, initial void ratio of soft soil, compression index, permeability index, initial permeability coefficient, drainage board spacing, drainage board width, and drainage board burial depth as parameters, an eight-dimensional parameter space is established, and multiple sets of working condition combinations covering the project area are generated through a space-filling sampling method.

[0012] S2. Establish nonlinear large-strain consolidation control equations and perform batch high-fidelity solutions: Based on the nonlinear characteristics of the compressibility and permeability of dredged silt soft soil evolving with consolidation, a two-dimensional large-strain consolidation control equation is constructed and solved using numerical methods; for each working condition, grid construction, coefficient updating, time stepping, and iterative solutions are completed to obtain the excess pore water pressure field at different times, and the porosity, permeability coefficient, degree of consolidation, and settlement are derived accordingly;

[0013] S3. Construct a unified format dataset required for operator learning: Perform unified spatial and temporal resampling on the calculation results of all working conditions, convert the results of different working conditions into a fixed-dimensional data structure, and standardize the parameters and physical quantities to form a structured input-output sample pair suitable for operator learning;

[0014] S4. Construct and train the DeepONet operator model: Construct a DeepONet operator model with a parametric branch network, a spatiotemporal backbone network, and an operator fusion layer. The branch network is used to extract the nonlinear coupling relationship between parameters. The backbone network adopts a structure with high-frequency feature encoding to characterize the drastic changes in the ultrapore water pressure field near the drainage plate and the long-term decay characteristics of the consolidation process. The operator fusion layer uses a low-rank structure to realize the mapping of the consolidation operators. Conditional constraints are applied during the model training process.

[0015] S5. Verify and deploy the operator model: Select parameter conditions that were not used in training to verify the model. After the error meets the engineering accuracy requirements, deploy the model as a prediction operator that runs independently on the computing device.

[0016] S6. Realize real-time prediction and engineering application of the entire consolidation process: Input any new parameter combination into the model to obtain the prediction results of the entire process, including pore water pressure field, permeability coefficient, void ratio, degree of consolidation, and surface settlement, and use them for optimization of drainage board layout schemes and evaluation of resource utilization after consolidation of dredged silt and soft soil.

[0017] As a further improvement of the present invention, in S1, the space-filling sampling method includes Latin hypercube sampling and Sobol sequence.

[0018] As a further improvement of the present invention, in S2, the consolidation control equation is:

[0019]

[0020] Where e0 is the initial void ratio of the soft soil, u is the excess pore water pressure, and x, z, and t are the spatial and temporal coordinates. For the initial effective stress, For effective stress, The initial permeability coefficient, The density of water, The compression index, This is the penetration index. ;

[0021] Based on the calculation results of excess pore water pressure, the void ratio is calculated by the following formula:

[0022] ;

[0023] The permeability coefficient is calculated by the following formula: Its relationship with the void ratio is as follows: ;

[0024] Calculate the soil settlement at time t using the following formula:

[0025] ,

[0026] h is the height of the dredged silt and soft soil, w is the width of the drainage board, and s is the spacing width of the drainage board.

[0027] In the formula, ,

[0028] i and j are the designations of nodes on the differential grid, where j = 0, ..., N z -1, i=0,...,N x -1, N x and N z G represents the number of differential grids in the x and z directions, respectively. s γ is the specific gravity of soil particles. w For soil weight, Δz = h / N z For grid width, The excess pore pressure value of the grid node in the j-th row and i-th column at the n-th time step;

[0029] The average degree of consolidation is calculated using the following formula:

[0030] ,

[0031] In the formula, In the formula, This represents the effective stress of the soil layer when consolidation is complete.

[0032] As a further improvement of the present invention, in the batch high-fidelity solution of S2, a unified numerical solution subroutine is constructed by using multiple sets of working condition combinations obtained by Latin hypercube sampling. This subroutine takes a single set of normalized parameter vectors as input, automatically completes mesh generation, nonlinear coefficient field update, time stepping and Newton iteration solution, and outputs the high-fidelity ultrapore water pressure-time-space distribution under the given working condition. By introducing a working condition cycle control module in the outer layer, the numerical solution subroutine is called one by one for all single sets of normalized parameter vectors to perform batch numerical calculation of the consolidation control equations in the multi-parameter space.

[0033] As a further improvement of the present invention, in S2, the consolidation control equation is discretized using a backward time discretization scheme and a conservation space discretization scheme.

[0034] As a further improvement of the present invention, S3 specifically includes:

[0035] The ultrapore water pressure field under each working condition is resampled according to a unified spatial grid and time node to form a fixed-dimensional three-dimensional array U(x,z,t). At the same time, physical quantities including ultrapore water pressure, void ratio, and permeability coefficient are normalized. For each working condition, the normalized parameter vector and the uniformly sampled ultrapore water pressure field are combined to form a pair of "input-output" samples to construct the training dataset for DeepONet. The training set and test set are divided according to a preset ratio.

[0036] As a further improvement of the present invention, in S3, the unified resampling of space and time adopts linear interpolation, piecewise linear interpolation or three-dimensional interpolation methods.

[0037] As a further improvement of the present invention, in S4, the execution processes of the parameter branch network, spatiotemporal backbone network, and operator fusion layer of the DeepONet operator model are as follows:

[0038] The branch network takes the normalized parameter vector as input, extracts the nonlinear coupling features between the operating parameters through a multi-layer fully connected network and a channel attention module, and outputs a feature vector of fixed length.

[0039] The backbone network takes spatiotemporal coordinates as input, introduces Fourier feature encoding to express the long-term decay characteristics of the high gradient region near the drainage board and the consolidation process, and obtains spatiotemporal feature vectors through a multilayer perceptron.

[0040] The operator fusion layer uses element-wise multiplication and weighted summation on the outputs of the branch network and the backbone network to perform a low-rank approximation on the target operator, thereby obtaining the predicted value of the superpore water pressure at the corresponding spatiotemporal point.

[0041] As a further improvement of the present invention, in S4, the condition constraints of the model training process include data fitting constraints, consolidation control equation residual constraints, boundary condition constraints, and initial condition constraints.

[0042] As a further improvement of the present invention, S5 specifically includes:

[0043] Several working conditions that were not included in the training were selected, and their parameters were input into the trained DeepONet model to obtain the predicted excess pore water pressure field, consolidation degree-time curve and surface settlement-time curve, and compared with the corresponding high-fidelity numerical results.

[0044] The accuracy of the model is quantitatively evaluated by indicators including spatiotemporal RMSE, consolidation deviation, and settlement deviation. At the same time, it is checked whether the prediction results meet the requirements of indicators including monotonic dissipation of excess pore water pressure, consistency of boundary conditions, and rationality of physical relationships.

[0045] When all indicators meet the preset engineering accuracy threshold, the network parameters are deployed as proxy model files and encapsulated as prediction operators with a "single function interface" to run on the computing device.

[0046] The beneficial effects of this invention are:

[0047] Compared with existing analytical methods, finite element methods, and simple data-driven models for the consolidation process of dredged silt and soft soil, this invention represents a number of fundamental breakthroughs in terms of technical system, data construction strategy, solution efficiency, and engineering deployability. Its key advancements are as follows:

[0048] (1) Existing methods usually only perform consolidation analysis under single or low-dimensional parameter conditions, and cannot simultaneously consider the multi-dimensional coupling of initial structure, compression characteristics, permeability evolution and drainage board layout parameters of soft soil. This invention constructs an eight-dimensional engineering parameter space consisting of vacuum negative pressure, initial void ratio of soft soil, compression index, permeability index, initial permeability coefficient, drainage board spacing, drainage board width and drainage board burial depth, and uses Latin hypercube sampling to generate 2000~5000 uniformly covered working conditions, achieving "full parameter domain coverage" and "extreme working condition robustness" that are unattainable by traditional methods.

[0049] (2) Conventional methods can only obtain nonlinear forms, while this invention obtains a fully expanded form.

[0050] (3) To address the problem of inconsistent grids under different working conditions, this invention proposes a unified resampling and normalization strategy, which transforms all working condition outputs into fixed-dimensional structures, achieving "end-to-end alignability" of operator learning and training, and completely solving the problem that traditional models have difficulty directly learning PDE outputs.

[0051] (4) Compared with traditional deep networks, the DeepONet operator model of the present invention introduces Fourier feature encoding in the backbone network to significantly enhance the expressive ability of the high gradient region in the neighborhood of the drainage board; and adopts channel attention mechanism in the branch network to accurately capture the parameter coupling relationship, thereby improving the operator approximation ability.

[0052] (5) Traditional finite element consolidation solutions take tens of minutes to several hours. The inference time of the operator model trained in this invention is in the millisecond level, which can be used for real-time monitoring, real-time early warning and real-time optimization design, which is impossible to achieve with existing methods.

[0053] (6) This invention can not only output the pressure field of excess pore water, but also calculate the spatiotemporal evolution of permeability coefficient, spatiotemporal evolution of porosity, degree of consolidation-time curve, and settlement-time curve in real time. It also supports repeated and rapid scanning of drainage board parameters, enabling rapid optimization of engineering design and quantitative determination of the feasibility of soft soil resource utilization. This overall framework is an original technology. Attached Figure Description

[0054] Figure 1 This is a flowchart of a rapid prediction method for consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning, according to the present invention.

[0055] Figure 2 This is a flowchart illustrating the parameter space definition and operating condition combination generation in an embodiment of the present invention;

[0056] Figure 3 This is a flowchart of high-fidelity finite element batch calculation in an embodiment of the present invention;

[0057] Figure 4 This is a flowchart of multi-dimensional physical field post-processing and dataset construction in an embodiment of the present invention;

[0058] Figure 5 This is a flowchart illustrating the structural design and training of the DeepONet proxy model in this embodiment of the invention.

[0059] Figure 6 This is a flowchart illustrating the verification and deployment of the proxy model in this embodiment of the invention;

[0060] Figure 7 This is a flowchart illustrating the implementation of prediction and dual-objective engineering applications in an embodiment of the present invention;

[0061] Figure 8 This is a schematic diagram of the consolidation model and calculation unit of the horizontal drainage board vacuum preloading soft soil in an embodiment of the present invention, (a) consolidation model, (b) calculation unit;

[0062] Figure 9 This is a schematic diagram of the discrete mesh of the calculation unit of the vacuum preloading soft soil consolidation model of the horizontal drainage board in an embodiment of the present invention;

[0063] Figure 10 This is a schematic diagram of the DeepONet operator network architecture in an embodiment of the present invention. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0065] This invention organically combines high-fidelity nonlinear large-strain consolidation numerical calculation with the DeepONet operator learning framework. It achieves an end-to-end mapping from "soil-drainage board parameter input" to "pore water pressure field, void ratio, permeability coefficient, degree of consolidation and settlement response throughout the entire process," reducing the solution time of complex consolidation equations from hours to milliseconds. This provides an efficient and deployable prediction method for optimizing the vacuum preloading design of horizontal drainage boards and for the resource utilization of dredged silt and soft soil.

[0066] To achieve the above objectives, the technical solution provided by this invention mainly includes the following steps and key contents:

[0067] like Figure 1 As shown, the present invention provides a method for rapid prediction of consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning, comprising the following steps:

[0068] S1. Construct a multidimensional consolidation control parameter space: Using vacuum negative pressure, initial void ratio of soft soil, compression index, permeability index, initial permeability coefficient, drainage board spacing, drainage board width, and drainage board burial depth as parameters, an eight-dimensional parameter space is established, and multiple sets of working condition combinations covering the project area are generated through a space-filling sampling method.

[0069] First, key parameters that dominate the nonlinear large-strain consolidation process of dredged silt and soft soil were identified, and a model was constructed based on vacuum negative pressure Q, initial void ratio of soft soil e0, and compressibility index C. c Penetration Index C k An eight-dimensional parameter space is constructed, comprising the initial permeability coefficient k0, the horizontal drainage board spacing s, the drainage board width w, and the drainage board burial depth h. The range of values ​​for each parameter is determined based on measured data and design experience from typical dredging and reclamation projects, ensuring that the parameter space covers both extremely soft soil conditions and relatively hard soil conditions. Then, spatially filled design methods such as Latin hypercube sampling and Sobol sequences are used to generate thousands of representative combinations of working conditions within the parameter space, ensuring uniform coverage of feasible working conditions within the eight-dimensional parameter space. Furthermore, sampling can be densified in parameter boundary areas to improve the model's robustness under extreme conditions.

[0070] S2. Establish nonlinear large-strain consolidation control equations and perform high-fidelity batch solutions: Based on the nonlinear characteristics of the compressibility and permeability of dredged silt soft soil evolving with consolidation, a two-dimensional large-strain consolidation control equation is constructed and solved using existing mature numerical methods such as finite element and finite difference methods. For each working condition, mesh construction, coefficient updating, time stepping, and iterative solution are completed to obtain the excess pore water pressure field at different times, and the porosity, permeability coefficient, degree of consolidation, and settlement are derived accordingly.

[0071] The nonlinear coefficients of the consolidation governing equations are dynamically updated based on changes in void ratio to reflect the nonlinear evolution of the permeability and compressibility of dredged silt soft soil. The consolidation governing equations are discretized using a backward time discretization scheme and a conservation-type spatial discretization scheme, forming an implicit nonlinear algebraic equation system.

[0072] Batch solving for multiple working conditions is achieved through automated scripts, including parameter reading, unified mesh generation, nonlinear coefficient field updating, iterative solving, and automatic result storage.

[0073] Based on the soil properties and drainage board layout information given in the parameter space, this invention establishes a two-dimensional nonlinear large-strain consolidation control equation that reflects the significant compressibility and nonlinear permeability of dredged silt soft soil. The equation considers the coupling relationship between excess pore water pressure dissipation and soil volumetric strain. The equation is solved numerically. Furthermore, using the excess pore water pressure calculation results from the equation, the evolution of porosity and permeability coefficient with time and depth can be calculated according to given formulas, thereby obtaining the consolidation degree-time curve and the surface settlement-time curve. This invention uses a unified numerical solution subroutine to automatically and iteratively solve all working condition combinations, achieving high-fidelity batch calculation of the consolidation control equation in a multi-parameter space, and storing the calculation results for each working condition in a structured format.

[0074] S3. Construct a unified format dataset required for operator learning: Perform unified spatial and temporal resampling on the calculation results of all working conditions, convert the results of different working conditions into a fixed-dimensional data structure, and standardize the parameters and physical quantities to form a structured input-output sample pair suitable for operator learning.

[0075] Unified resampling employs linear interpolation, piecewise linear interpolation, or three-dimensional interpolation methods to ensure that the excess pore water pressure field under all operating conditions has consistent spatial and temporal dimensions.

[0076] Given that numerical discrete grids may differ under different operating conditions, this invention resamples the excess pore water pressure field for each operating condition using a unified spatial grid and time nodes, forming a fixed-dimensional three-dimensional array. Simultaneously, physical quantities such as excess pore water pressure, void ratio, and permeability coefficient are normalized to eliminate numerical instability caused by dimensional differences. For each operating condition, the normalized parameter vector is... With uniformly sampled excess pore water pressure field A pair of "input-output" samples is formed to construct a training dataset that can be directly input into DeepONet, and the training set and test set are divided according to a preset ratio to evaluate the generalization ability of the operator model.

[0077] S4. Construct and train the DeepONet operator model: Construct a DeepONet operator model with a parametric branch network, a spatiotemporal backbone network, and an operator fusion layer. The branch network is used to extract the nonlinear coupling relationship between parameters. The backbone network adopts a structure with high-frequency feature encoding to characterize the drastic changes in the ultrapore water pressure field near the drainage plate and the long-term decay characteristics of the consolidation process. The operator fusion layer uses a low-rank structure to realize the mapping of the consolidation quantifier. During the model training process, data fitting constraints, consolidation control equation residual constraints, boundary condition constraints, and initial condition constraints are applied simultaneously.

[0078] This invention employs DeepONet as the operator learning framework for the consolidation process, approximating the "operating parameters → consolidation process response" as a high-dimensional operator mapping. DeepONet comprises a branch network, a backbone network, and an operator fusion layer.

[0079] Branch networks with normalized parameter vectors As input, the nonlinear coupling features between operating parameters are extracted through a multi-layer fully connected network and a channel attention module, and a fixed-length feature vector is output. The branch network contains an attention mechanism to enhance the ability to distinguish the influence of different parameters on the consolidation process.

[0080] The backbone network takes spatiotemporal coordinates (t,x,z) as input and introduces Fourier feature encoding to enhance its ability to express the long-term decay characteristics of the high gradient region near the drainage board and the consolidation process. It also obtains spatiotemporal feature vectors through a multilayer perceptron. The backbone network adopts an input structure with frequency encoding to enhance its ability to express the long-term decay behavior of the high gradient region near the drainage board and the consolidation process.

[0081] The operator fusion layer uses element-wise multiplication and weighted summation on the outputs of the branch network and the backbone network to achieve a low-rank approximation of the target operator, thereby obtaining the predicted value of the superpore water pressure at the corresponding spatiotemporal point. The operator fusion layer adopts a low-rank structure, which allows the solidified operator to be expressed in the form of a multiplicative combination of parametric features and spatiotemporal features.

[0082] During training, this invention not only employs data fitting loss to constrain the consistency between DeepONet output and high-fidelity numerical solutions, but also selects collocation points in the spatiotemporal domain to construct residual loss, boundary condition loss, and initial condition loss for the consolidation control equations, explicitly introducing physical constraints into the network training process. By combining Adam pre-training with L-BFGS fine-tuning, the total loss function is gradually reduced, enabling the obtained network parameters to accurately approximate the operator behavior of the high-fidelity numerical solver.

[0083] The training process includes residual constraints on the consolidation control equations to improve the model's physical consistency and predictive stability under unseen operating conditions. Independent loss terms with Dirichlet and Neumann boundary conditions are further included during training. The model training employs a combination of adaptive learning rate optimization and second-order optimization methods to improve convergence speed and model accuracy.

[0084] S5. Verify and deploy the operator model: Select parameter conditions that were not used in training to verify the model. After the error meets the engineering accuracy requirements, deploy the model as a lightweight prediction operator that can run independently on computing devices such as CPUs, GPUs, or edge devices.

[0085] This invention selects several untrained operating conditions and inputs their parameters into a pre-trained DeepONet operator model to obtain predicted excess pore water pressure fields, consolidation degree-time curves, and surface settlement-time curves, which are then compared with the corresponding high-fidelity numerical results. The model accuracy is quantitatively evaluated using indicators such as spatiotemporal RMSE, consolidation degree deviation, and settlement deviation. Simultaneously, it checks whether the prediction results meet requirements such as monotonic dissipation of excess pore water pressure, consistency of boundary conditions, and rationality of physical relationships. When all the above indicators meet the preset engineering accuracy threshold, the network parameters are deployed as a proxy model file and encapsulated as a prediction operator with a "single-function interface," which can run at millisecond speeds on ordinary CPUs, handheld terminals, edge computing devices, or cloud servers.

[0086] S6. Realize real-time prediction of the entire consolidation process and its engineering application: By inputting any new parameter combination into the model, the prediction results of the entire process, such as pore water pressure field, permeability coefficient, void ratio, degree of consolidation, and surface settlement, can be obtained in milliseconds. These results can be used for the optimization of drainage board layout schemes and the evaluation of resource utilization after the consolidation of dredged silt and soft soil.

[0087] The validated DeepONet operator model outputs can be used for real-time optimization of parameters such as drainage board spacing, drainage board placement depth, and vacuum preloading pressure to meet target consolidation or settlement control requirements. The permeability coefficient and void ratio distribution outputs of the DeepONet operator model can be used to determine whether the consolidated dredged silt and soft soil meet the resource utilization indicators for road fill, embankment fill, or other engineering applications.

[0088] In practical engineering applications, given new physical property parameters of dredged silt and soft soil and a horizontal drainage board layout scheme, this invention does not require reconstructing the mesh or performing numerical iterations. It only needs to input the parameter vectors into the deployed DeepONet operator model to quickly obtain the spatiotemporal distribution of pore water pressure field, void ratio, and permeability coefficient, as well as the consolidation degree-time curve and surface settlement-time curve. Based on these prediction results, on the one hand, it can be used for the rapid optimization of design parameters such as horizontal drainage board spacing and burial depth, and the adjustment of loading-unloading schemes during construction, achieving proactive control over post-construction settlement and consolidation rate; on the other hand, it can be used to evaluate whether the permeability coefficient and void ratio distribution of consolidated soft soil under different working conditions meets the filler indicators for roadbeds, embankments, etc., thereby quantitatively determining the resource utilization potential of dredged silt and soft soil.

[0089] Through the above steps, this invention, while maintaining the physical reality of nonlinear large-strain consolidation, migrates the solution process of complex consolidation control equations from high-cost traditional numerical simulation to a lightweight operator model, realizing high-fidelity, multi-condition, and second-level response rapid prediction of consolidation and settlement. This provides a new technical path for design optimization and decision support in the treatment of dredged silt and soft soil by vacuum preloading of horizontal drainage boards.

[0090] The following detailed description, in conjunction with embodiments of the present invention, provides a nonlinear large-strain consolidation and rapid settlement prediction method for dredged silt and soft soil based on operator learning using vacuum preloading of horizontal drainage boards. Those skilled in the art should understand that equivalent substitutions or adjustments can be made to the following embodiments without departing from the core ideas of the present invention, and all such substitutions or adjustments fall within the scope of protection of the present invention.

[0091] Example 1: A rapid prediction method for nonlinear large-strain consolidation and settlement of horizontal drainage board dredged silt and soft soil based on operator learning, combined with... Figures 1 to 10 As shown.

[0092] This embodiment provides a rapid consolidation-settlement prediction method for dredged silt and soft soil treatment projects. By combining high-fidelity nonlinear large-strain consolidation numerical calculations with an operator learning framework, the prediction of pore water pressure field, permeability coefficient, void ratio, degree of consolidation, and settlement development patterns is shortened from hours of traditional numerical simulations to seconds. This provides an efficient and reliable technical means for foundation treatment design optimization and resource utilization evaluation. The method of this invention mainly includes the following six steps:

[0093] S1. Parameter space definition and operating condition combination generation.

[0094] S11. Determine the parameter type:

[0095] This invention clarifies the key parameter categories that dominate the nonlinear consolidation process of dredged silt and soft soil, and constructs a corresponding eight-dimensional parameter space. This invention selects four soil property parameters characterizing the physical properties of soft soil, and three construction parameters related to dredging and drainage boards, specifically including:

[0096] (1) Initial void ratio e0 of soft soil;

[0097] (2) Compression index C c ;

[0098] (3) Penetration index C k (Describe the sensitivity of the permeability coefficient to changes in the void ratio);

[0099] (4) Initial permeability coefficient k0;

[0100] (5) Vacuum preloading spacing s of horizontal drainage board;

[0101] (6) Width w of the drainage board;

[0102] (7) Drainage board burial depth h;

[0103] (8) Vacuum pre-compression negative pressure Q applied to the horizontal drainage plate.

[0104] S12. Determine the range of values:

[0105] To enhance the model's applicability and extrapolation capability, the engineering value ranges for each parameter were determined based on measured data and design experience from multiple dredging and reclamation projects both domestically and internationally, as follows:

[0106] The value of e0 ranges from 1.8 to 4.0;

[0107] C c The value range is 0.4 to 1.8;

[0108] C k The value range is 0.2 to 1.2;

[0109] The value of k0 is in the range of 1×10. -9 ~1×10 -6 m / s;

[0110] The value of s ranges from 0.5 to 5.0 m;

[0111] The value of w ranges from 0.05 to 0.2m;

[0112] The value of h ranges from 1 to 5m;

[0113] The value of Q ranges from 50 to 150 kPa.

[0114] S13. Generate combined operating conditions:

[0115] Within the aforementioned eight-dimensional parameter space, several sets of working condition combinations are generated using space-filling experimental design methods such as Latin hypercube sampling and Sobol sequences. This method samples each parameter dimension in a stratified manner with equal probability, ensuring uniform distribution and sufficient coverage of the samples throughout the space. Optionally, denser sampling is added near the parameter value boundaries to enhance the robustness of the surrogate model under extremely soft or relatively hard soil conditions. In this embodiment, approximately 2000–5000 representative working condition combinations are generated, providing input conditions for subsequent high-fidelity numerical simulations.

[0116] S2: High-fidelity finite element batch calculation.

[0117] S21. Establish the consolidation governing equations:

[0118] The consolidation control equations used in this invention can be mathematically summarized as a class of binonlinear diffusion equations, the general form of which can be derived from existing literature, i.e.

[0119]

[0120] In the formula, u is the excess pore water pressure, x, z, and t are the spatial and temporal coordinates, and k0 is the initial permeability coefficient. It is water-weighted. For the initial effective stress, I c and I k These are the compression and penetration indices, respectively. .

[0121] To facilitate the writing of difference programs or future use of PINN to solve this equation, it needs to be written in its complete expansion form as follows:

[0122]

[0123] In the formula, e is the void ratio of soft soil, e0 is the initial void ratio of soft soil, and u is the excess pore water pressure. For the initial effective stress, For effective stress, The initial permeability coefficient, The density of water, The compression index, This is the penetration index; .

[0124] S22. Initial boundary condition definition:

[0125] The computational domain is rectangular, mathematically represented as: With the top left corner as the origin, z is positive downwards. w is the width of the drainage board, b is the spacing between the drainage boards, and L is the width of the calculation unit.

[0126] Initial conditions, i.e.

[0127] The boundaries of the top and bottom drainage panels are the Dirichlet boundaries, respectively.

[0128] ,

[0129] The bottom non-drained boundary is the Newman boundary, which is...

[0130]

[0131] The left and right boundaries are the Newman boundaries, respectively.

[0132]

[0133] S23. Solving the equation:

[0134] This equation is a strongly nonlinear equation, and finding an analytical solution would be extremely difficult or even impossible. Numerical methods can be used to solve it, such as the finite element method or the finite difference method. The finite element method for solving partial differential equations often utilizes mature commercial software such as COMSOL or FLEXPDE; inputting the equation form, coefficients, and initial boundary conditions allows for rapid solutions. The finite difference method for solving partial differential equations often uses custom boundary code, such as in MATLAB or Python, and employs the Alternating Direction Implicit Difference (ADI) method or the more accurate semi-implicit Picard nonlinear iterative method to discretize and solve the equation. These two types of numerical solution methods are well-known in the field and are not the core of this invention; therefore, they are not detailed here.

[0135] S24. Calculate void ratio, permeability coefficient, settlement, and degree of consolidation:

[0136] Based on the calculation results of excess pore water pressure, the void ratio is calculated by the following formula:

[0137] ,

[0138] The permeability coefficient is calculated by the following formula:

[0139] The relationship between porosity and other factors is as follows: ;

[0140] As can be seen from the above two equations, after obtaining the distribution of excess pore water pressure, the spatiotemporal distribution characteristics of the filler permeability coefficient and porosity that are of interest in the landfill project can be calculated.

[0141] Calculate the soil settlement at time t using the following formula.

[0142] ,

[0143] h is the height of the dredged silt and soft soil, w is the width of the drainage board, and s is the spacing width of the drainage board.

[0144] In the formula, ,

[0145] i and j are the designations of nodes on the differential grid, where j = 0, ..., N z -1, i=0,...,N x -1, N x and N z G represents the number of differential grids in the x and z directions, respectively. s γ is the specific gravity of soil particles. w For soil weight, Δz = h / N z For grid width, Let be the excess pore pressure value of the grid node in row j and column i at time step n. These only represent the results of the expression when solving the governing equations using the finite difference method.

[0146] Calculate the average degree of consolidation using the following formula

[0147] ,

[0148] In the formula, In the formula, This represents the effective stress of the soil layer when consolidation is complete.

[0149] S25. Batch numerical computation:

[0150] The above constitutes a complete and directly reproducible implementation path for solving nonlinear large-strain finite difference equations in soft soil. Within the common knowledge of those skilled in the art, solving a system of nonlinear algebraic equations using the finite difference method does not require writing out the expansion results for every term; simply clarifying the construction of the residuals and the Jacobian matrix ensures the deterministic and reproducible nature of the solution. The discrete structure, the source of nonlinear terms, the boundary condition handling method, and the iterative format of this invention have all been provided, sufficient for those skilled in the art to implement the solution process without creative effort. Therefore, this invention possesses legally recognized "sufficient disclosure" and "implementability." A similar principle applies to the finite element method.

[0151] In a preferred embodiment of the invention, a unified numerical solution subroutine is constructed for multiple (e.g., 1000) combinations of working conditions obtained through Latin hypercube sampling. This subroutine uses a single set of normalized parameter vectors. As input, it automatically completes mesh generation, nonlinear coefficient field update, time stepping and Newton iteration solution, and outputs high-fidelity ultrapore water pressure-time-space distribution under given working conditions.

[0152] Based on this, by introducing a working condition cycle control module in the outer layer, all The above-mentioned solution subroutines are called one by one to realize the batch numerical calculation of the consolidation control equations in the multi-parameter space. The solution results for each working condition (including excess pore water pressure field, permeability coefficient field, void ratio distribution, degree of consolidation-time curve, and surface settlement-time curve, etc.) are automatically stored as structured data files for subsequent construction of operator learning datasets.

[0153] S3: Multi-dimensional physical field post-processing and dataset construction.

[0154] This embodiment refines step S3, "Post-processing of multi-dimensional physical fields and construction of datasets," focusing on how to convert the high-fidelity pore water pressure field obtained from batch calculations using finite element / finite difference methods into a unified format training and testing dataset that DeepONet can directly accept. This embodiment ensures that those skilled in the art can construct an end-to-end dataset structure suitable for operator learning by following the instructions.

[0155] S31. Input Data Sources and Batch Generation:

[0156] Step S2 has been based on different parameter combinations Perform batch finite element / finite difference solutions. For each set of parameters The pore water pressure field under the corresponding time history was obtained. ,

[0157] All calculation results are automatically saved to a unified data directory structure:

[0158] / dataset /

[0159] / case_001 / u(x,z,t)

[0160] / case_002 / u(x,z,t) ...

[0162] / case_N / u(x,z,t)

[0163] Ensure that the post-processing stage can automatically traverse and process all operating conditions.

[0164] S32. Unified Spatiotemporal Grid Resampling:

[0165] Since the finite element mesh may differ under different operating conditions, DeepONet requires all input data to correspond to a "fixed spatiotemporal mesh" of uniform dimensions. Therefore, while ensuring computational accuracy, this embodiment sets a uniform sampling mesh:

[0166] Number of nodes in the horizontal direction N x =40;

[0167] Number of nodes in the depth direction Nz =40;

[0168] Number of time nodes N t =50;

[0169] And perform three-dimensional resampling on each group u⁽ⁿ⁾ to obtain:

[0170] The resampling algorithm can be piecewise linear interpolation (FDM).

[0171] S33. Normalization ensures network trainability.

[0172] To avoid inconsistencies in the physical quantity scales between different operating conditions, this embodiment uses min-max normalization to process the excess pore water pressure data:

[0173]

[0174] All after normalization The data values ​​are all distributed between [0,1], which improves the numerical stability of operator learning.

[0175] S34. Structured Representation of Input Vectors

[0176] Each set of operating conditions corresponds to a unique set of parameter vectors. And perform normalization: Normalized Stored as a fixed-length 8×1 vector .

[0177] S35. Constructing an input-output paired dataset for operator learning.

[0178] The goal of this step is to construct a training dataset with a completely uniform format that can be directly input into DeepONet. For each working condition n, the final data structure is as follows:

[0179] (enter) , The set of natural numbers

[0180] (Output)

[0181] Therefore, a single training sample can be represented as:

[0182] U norm The output of the model is to uniformly sample the pore pressure field.

[0183] All samples constitute the training set:

[0184] Dataset={Sample⁽¹⁾,Sample⁽²⁾,…,Sample⁽ᴺ⁾}

[0185] N can be taken as 2000~5000.

[0186] S36. Divide the training set and the test set:

[0187] This embodiment uses an 8:2 division method: 80% of the working conditions are used as the training set, and 20% of the working conditions are used as the test set.

[0188] test set It does not participate in operator training and is used to verify the generalization ability of DeepONet.

[0189] The dataset constructed in this step of the embodiment has the following characteristics:

[0190] (1) All operating conditions are represented in a unified spatiotemporal dimension;

[0191] (2) All input parameters μ and output excess pore water pressure field U have been normalized. Their symbols after normalization are expressed as follows: and "norm" is an abbreviation for "normalization".

[0192] (3) The data format is fully aligned and can be directly fed into the DeepONet branch network and backbone network;

[0193] (4) It can be used for end-to-end operator learning and training without additional manual processing.

[0194] This embodiment ensures that DeepONet can effectively learn the mapping relationship from parameter space μ to the full field U(x,z,t) of ultrapore water pressure, providing a standardized data foundation for subsequent S4 operator training.

[0195] S4: Structural design and training of the DeepONet proxy model.

[0196] Because the consolidation control equation of this invention has the following significant characteristics: (1) the excess pore water pressure field has a significant "vertical step dominated by the drainage plate control boundary"; (2) the coupling of nonlinear permeability coefficient and effective stress leads to a strong nonlinear gradient in the flux direction; (3) the consolidation process has long-term attenuation; and (4) the degree of consolidation-settlement curve has a significant S-shaped feature. Therefore, based on the traditional DeepONet framework, this invention enhances the branch network and backbone network structure respectively, enabling them to capture the global structural features of the aforementioned nonlinear consolidation.

[0197] S41. Operator Mapping and Network Structure Definition:

[0198] Define the working condition parameter vector The spacetime point is The DeepONet approximation operator is: Network output is denoted as ,in For all network parameters.

[0199] S42. Network Architecture Establishment:

[0200] DeepONet consists of branch networks, a backbone network, and a fusion layer. The branch networks output feature vectors. The backbone network outputs feature vectors. The fusion layer uses an inner product approach.

[0201] This form can be viewed as a pair of operators. rank Approximate expansion.

[0202] In a preferred embodiment, the branch network structure includes:

[0203] Input layer B_in: 8 neurons (corresponding to μ); Hidden layer B_h1: 64 neurons, activation function ReLU; Hidden layer B_h2: 64 neurons, activation function ReLU; Channel attention module CA: its key matrix W_K, query matrix W_Q, and value matrix W_V are all 64×64; Output layer B_out: F-dimensional feature vector (in this embodiment, F=32).

[0204] The above structure can be expressed as: b(μ) = B(μ) ∈ ℝ F The CA module is used to enhance the ability to capture the differences in the family of spatiotemporal evolution curves of excess pore water pressure caused by nonlinear coupling between parameters.

[0205] In a preferred embodiment, the backbone network structure includes:

[0206] Its input is a space-time point. This represents the query point required for the consolidation response. It exhibits clear separability and long-term decay characteristics in both the vertical and temporal dimensions. Traditional multilayer perceptrons can only capture local spatial features, thus making it difficult to reproduce the two types of features: "local strong gradient of the drainage board + global diffusion decay".

[0207] To this end, the present invention introduces Fourier Feature Encoding into the backbone network to enhance the network’s sensitivity to high-frequency gradients (e.g., gradients near the drainage board).

[0208] The backbone network structure may include:

[0209] Input layer Input vector First, Fourier feature mapping , forming an extended dimension vector Hidden layer 64 neurons; hidden layer 64 neurons; hidden layer 32 neurons; output layer : F-dimensional feature vector (F=32, aligned with the branch network), i.e.:

[0210] Fourier feature mapping uses: ,

[0211] Where B is a random or trainable frequency matrix, used to improve the ability to represent local high gradients in the consolidated field.

[0212] In a preferred embodiment, the operator fusion layer structure includes:

[0213] The operator fusion layer adopts an element-wise multiplication and weighted summation structure:

[0214] This is the low-rank decomposition form of the operator approximation.

[0215] S43. Determine the composition of DeepONet input and output vectors.

[0216] Branch network input:

[0217] .

[0218] Backbone network input:

[0219] .

[0220] The backbone network is formed after Fourier encoding:

[0221] ,

[0222] The final DeepONet output is the predicted value of excess pore water pressure:

[0223] .

[0224] S44. Constructing Datasets and Defining Symbols:

[0225] In the offline phase, each set of working conditions is obtained using the finite difference or finite element method. Corresponding high-precision numerical solution The training set was obtained by sampling at all operating conditions and all discrete points:

[0226] In the formula N data represents the number of discrete points selected, and represents the actual dataset.

[0227] To further improve prediction accuracy, consistency constraints of the governing equations and boundary conditions are also introduced into the loss function. That is, several collocation points are selected in the spatiotemporal domain and parameter domain to form a set of PDE residual constraint points:

[0228]

[0229] N data N represents the number of discrete data points (collocation points) used during DeepONet network training. PDE This indicates the number of training points selected on the PDE residual.

[0230] S45. Define the mathematical expressions for each loss function.

[0231] (1) Data fitting loss

[0232]

[0233] (2) PDE residual loss

[0234] Automatic differential calculation is used in the network output. Isoders, constructing PDE residuals:

[0235]

[0236] in The residual loss is In the formula, N PDE The number of sampling points selected for the equation.

[0237] (3) Boundary condition loss

[0238] Among them, the Dirichlet boundary point set superior:

[0239] In the formula, ND represents the number of sampling points selected on the Dirichlet boundary.

[0240] Neumann boundary point set Above, set The direction of the outer normal to the boundary:

[0241] In the formula N N The number of sampling points selected on the Dirichlet boundary.

[0242] The total boundary loss is

[0243] .

[0244] (4) Initial condition loss

[0245] Initial time Point set on superior:

[0246] In the formula, NIC represents the number of sampling points selected at the initial time.

[0247] (5) Total loss function and training process

[0248] Based on the above, the total loss function is defined as follows:

[0249] ,

[0250] in These are weight coefficients, which are hyperparameters of DeepONet and need to be determined based on the modeler's experience before training.

[0251] S46. Training Operator Model

[0252] (1) Based on sampling in eight-dimensional parameter space The control equations are solved using the finite difference or finite element method to obtain offline high-fidelity numerical solutions;

[0253] (2) Construct the data point and PDE residual point set according to the consolidation control equation;

[0254] (3) Initialize DeepONet parameters Using the Adam optimizer Perform pre-training;

[0255] (4) Based on pre-training, second-order optimization methods such as L-BFGS are used to further reduce the speed. until convergence;

[0256] (5) Validate the model using a parameter set not used in training, calculate the error of the excess pore water pressure field, the RMSE of the representative spatiotemporal section, and the error of the consolidation degree-time curve. If the preset accuracy is met, then... The intelligent agent operator model of this invention is deployed.

[0257] S5: Validation and deployment of the proxy model.

[0258] In this embodiment, step S5 is used to verify the consolidation prediction proxy model built based on DeepONet, and after meeting the accuracy requirements, deploy it as a lightweight prediction operator that can be directly used in engineering applications.

[0259] S51. Select the validation dataset:

[0260] First, select M new working conditions from the eight-dimensional parameter space that were not involved in the training. Substituting this into a high-fidelity finite element / finite difference consolidation model yields a "verification baseline solution" that differs from the training set. .

[0261] S52. Verify the accuracy of the operator prediction results:

[0262] Then, the same set of parameters Input a pre-trained DeepONet model to generate surrogate model predictions. The consistency between the two can be compared using the following error metrics:

[0263] Spacetime RMSE Indicator:

[0264] ,

[0265] Consolidation degree – time curve deviation:

[0266] ,

[0267] Surface subsidence deviation:

[0268] .

[0269] If the above error indicators meet the preset accuracy thresholds (e.g., RMSE < 3%, ΔU < 3%, Δs < 3%), then the DeepONet proxy model is determined to have sufficient engineering accuracy.

[0270] To further ensure stability across the entire parameter domain, this invention employs the following pre-deployment verification measures:

[0271] (1) Boundary consistency verification: check Whether the Dirichlet condition and Neumann boundary constraints of the drainage board are automatically satisfied;

[0272] (2) Stability criterion: Verify that the predicted excess pore water pressure sequence satisfies The consolidation monotonicity;

[0273] (3) Physical consistency verification: The effective stress and permeability coefficient sequence is back-derived from the predicted excess pore water pressure to check whether it meets the requirements. The double logarithmic nonlinear physical correlation.

[0274] S53. Deployment of predictive operators for dredging and soft soil treatment projects:

[0275] Through the above three layers of verification, this invention ensures that the DeepONet model can be used as a deployable engineering prediction operator.

[0276] After successful verification, the present invention will train the network parameters. The deployment is as a model file, and the branch network B, the backbone network T, and the operator fusion module are encapsulated as a "single-function interface," which is called as follows:

[0277] ,

[0278] The model can run at millisecond speeds on local CPUs, embedded terminals, or edge computing devices.

[0279] S6: Real-time prediction and bi-objective engineering applications.

[0280] Step S6 is used to deploy the DeepONet proxy model to the actual dredged silt and soft soil consolidation engineering scenario, to achieve second-level consolidation prediction, and to provide decision support for the two engineering objectives of "construction design guidance" and "resource utilization evaluation".

[0281] S61. Engineering Prediction Operator Call:

[0282] When new soil and drainage board parameters are input into the engineering design At this time, there is no need to rebuild the mesh or run any numerical iterations; simply call:

[0283] ,

[0284] The following full-field output can be obtained in approximately 5–20 milliseconds:

[0285] (1) Three-dimensional distribution of excess pore water pressure with depth-time ;

[0286] (2) Spatiotemporal distribution of porosity

[0287] ,in , which is the effective stress.

[0288] (3) Spatiotemporal distribution of permeability coefficient

[0289] ,

[0290] (4) Prediction of surface subsidence

[0291] ,

[0292] (5) Consolidation degree-time curve

[0293] ,

[0294] In the formula, In the formula, This represents the effective stress of the soil layer when consolidation is complete.

[0295] The entire process does not require finite difference solution procedures such as mesh generation and iterative calculation.

[0296] S62. Predictive Target 1: Construction Design Guidance.

[0297] The proxy model of this invention can be directly used to optimize construction layout parameters (drainage board spacing s, reinforcement depth h). On-site technicians can set constraints that meet settlement limits, such as:

[0298] ,

[0299] Then, the optimal combination of s and h is determined by fast scanning (GridSearch) or gradient search.

[0300] In addition, during the construction period, real-time monitoring of excess pore water pressure data can be utilized. The data is input into a proxy model to predict future consolidation states, enabling: early warning of post-construction settlement; dynamic optimization of drainage board spacing; and proactive adjustment of loading-unloading time windows.

[0301] S63. Prediction Objective Two: Assessment of Resource Utilization Potential.

[0302] This invention can be based on prediction and The following evaluation indicators will be automatically generated:

[0303] (1) The change in permeability coefficient before and after the target consolidation time is reached

[0304] ,

[0305] (2) Pore ratio distribution characteristics after consolidation

[0306] ,

[0307] (3) Whether it meets the threshold values ​​for embankment fill or surcharge soil, for example:

[0308] , ,

[0309] If the threshold is met, the dredged silt and soft soil are deemed to have the potential for resource utilization; if not, the improvement effect under different schemes can be simulated by modifying μ (e.g., increasing w or decreasing h or s).

[0310] The proxy model of this invention can be deployed on: edge servers at offshore reclamation construction sites; foundation treatment construction control systems; underground engineering information management platforms; and handheld mobile terminals (tablets, laptops).

[0311] The prediction process requires no mesh generation, no iterative solution, and no finite element solver; it relies solely on a lightweight neural network to achieve real-time consolidation prediction.

[0312] Through the above structure, the DeepONet constructed by this invention can reproduce the spatiotemporal behavior of high-fidelity solutions of solidified PDEs with extremely low inference cost (millisecond level), realize operator-level mapping of "parameters → the entire solidified spatiotemporal field", and provide a high-precision, deployable surrogate model for real-time prediction in engineering applications.

[0313] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A rapid prediction method for consolidation settlement of horizontally vacuum preloaded soft soil based on operator learning, characterized in that, Includes the following steps: S1. Construct a multidimensional consolidation control parameter space: Using vacuum negative pressure, initial void ratio of soft soil, compression index, permeability index, initial permeability coefficient, drainage board spacing, drainage board width, and drainage board burial depth as parameters, an eight-dimensional parameter space is established, and multiple sets of working condition combinations covering the project area are generated through a space-filling sampling method. S2. Establish nonlinear large-strain consolidation control equations and perform batch high-fidelity solutions: Based on the nonlinear characteristics of the compressibility and permeability of dredged silt soft soil evolving with consolidation, a two-dimensional large-strain consolidation control equation is constructed and solved using numerical methods; for each working condition, grid construction, coefficient updating, time stepping, and iterative solutions are completed to obtain the excess pore water pressure field at different times, and the porosity, permeability coefficient, degree of consolidation, and settlement are derived accordingly; S3. Construct a unified format dataset required for operator learning: Perform unified spatial and temporal resampling on the calculation results of all working conditions, convert the results of different working conditions into a fixed-dimensional data structure, and standardize the parameters and physical quantities to form a structured input-output sample pair suitable for operator learning; S4. Construct and train the DeepONet operator model: Construct a DeepONet operator model with a parametric branch network, a spatiotemporal backbone network and an operator fusion layer. The branch network is used to extract the nonlinear coupling relationship between parameters. The backbone network adopts a structure with high-frequency feature encoding to characterize the drastic changes in the pressure field of the superpore water near the drainage plate and the long-term decay characteristics of the consolidation process. The operator fusion layer realizes the mapping of the consolidation operator with a low-rank structure. And apply conditional constraints during model training; S5. Verify and deploy the operator model: Select parameter conditions that were not used in training to verify the model. After the error meets the engineering accuracy requirements, deploy the model as a prediction operator that runs independently on the computing device. S6. Realize real-time prediction of the entire consolidation process and its engineering application: Input any new parameter combination into the model to obtain the prediction results of the entire process, including pore water pressure field, permeability coefficient, void ratio, degree of consolidation, and surface settlement, and use them for optimization of drainage board layout schemes and evaluation of resource utilization after consolidation of dredged silt and soft soil.

2. The method for rapid prediction of consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, In S1, the space-filling sampling methods include Latin hypercube sampling and Sobol sequence.

3. The method for rapid prediction of consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, In S2, the consolidation governing equation is: ， Where e0 is the initial void ratio of the soft soil, u is the excess pore water pressure, and x, z, and t are the spatial and temporal coordinates. For the initial effective stress, For effective stress, The initial permeability coefficient, The density of water, The compression index, This is the penetration index. ; Based on the calculation results of excess pore water pressure, the void ratio is calculated by the following formula: ； The permeability coefficient is calculated by the following formula: Its relationship with the void ratio is as follows: ; Calculate the soil settlement at time t using the following formula: ， h is the height of the dredged silt and soft soil, w is the width of the drainage board, and s is the spacing width of the drainage board. In the formula, ; i and j are the designations of nodes on the differential grid, where j = 0, ..., N z -1, i=0,...,N x -1, N x and N z G represents the number of differential grids in the x and z directions, respectively. s γ is the specific gravity of soil particles. w For soil weight, Δz = h / N z For grid width, The excess pore pressure value of the grid node in the j-th row and i-th column at the n-th time step; The average degree of consolidation is calculated using the following formula: ， In the formula, In the formula, This represents the effective stress of the soil layer when consolidation is complete.

4. The rapid prediction method for consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, In the high-fidelity batch solution of S2, a unified numerical solution subroutine is constructed by using multiple combinations of working conditions obtained through Latin hypercube sampling. This subroutine takes a single set of normalized parameter vectors as input, automatically completes mesh generation, nonlinear coefficient field update, time stepping and Newton iteration solution, and outputs the high-fidelity ultrapore water pressure-time-space distribution under the given working conditions. By introducing a working condition cycle control module in the outer layer, the numerical solution subroutine is called one by one for all single sets of normalized parameter vectors to perform batch numerical calculation of the consolidation control equations in the multi-parameter space.

5. The rapid prediction method for consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, In S2, the consolidation control equations are discretized using a backward time discretization scheme and a conservation space discretization scheme.

6. The rapid prediction method for consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, S3 specifically includes: The ultrapore water pressure field under each working condition is resampled according to a unified spatial grid and time node to form a fixed-dimensional three-dimensional array U(x,z,t). At the same time, physical quantities including ultrapore water pressure, void ratio, and permeability coefficient are normalized. For each working condition, the normalized parameter vector and the uniformly sampled ultrapore water pressure field are combined to form a pair of "input-output" samples to construct the training dataset for DeepONet. The training set and test set are divided according to a preset ratio.

7. The method for rapid prediction of consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, In S3, the unified resampling of space and time adopts linear interpolation, piecewise linear interpolation, or three-dimensional interpolation methods.

8. The method for rapid prediction of consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, In S4, the execution processes of the parameter branch network, spatiotemporal backbone network, and operator fusion layer of the DeepONet operator model are as follows: The branch network takes the normalized parameter vector as input, extracts the nonlinear coupling features between the operating parameters through a multi-layer fully connected network and a channel attention module, and outputs a fixed-length feature vector. The backbone network takes spatiotemporal coordinates as input, introduces Fourier feature encoding to express the long-term decay characteristics of the high gradient region near the drainage board and the consolidation process, and obtains spatiotemporal feature vectors through a multilayer perceptron. The operator fusion layer uses element-wise multiplication and weighted summation on the outputs of the branch network and the backbone network to perform a low-rank approximation on the target operator, thereby obtaining the predicted value of the superpore water pressure at the corresponding spatiotemporal point.

9. The method for rapid prediction of consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, In S4, the constraints of the model training process include data fitting constraints, consolidation control equation residual constraints, boundary condition constraints, and initial condition constraints.

10. The method for rapid prediction of consolidation settlement of horizontal vacuum preloaded soft soil based on operator learning according to claim 1, characterized in that, S5 specifically includes: Several working conditions that were not included in the training were selected, and their parameters were input into the DeepONet operator model that had been trained to obtain the predicted excess pore water pressure field, consolidation degree-time curve and surface settlement-time curve, and compared with the corresponding high-fidelity numerical results. The accuracy of the model is quantitatively evaluated by indicators including spatiotemporal RMSE, consolidation deviation, and settlement deviation. At the same time, it is checked whether the prediction results meet the requirements of indicators including monotonic dissipation of excess pore water pressure, consistency of boundary conditions, and rationality of physical relationships. When all indicators meet the preset engineering accuracy threshold, the network parameters are deployed as proxy model files and encapsulated as prediction operators with a single function interface, and then run on the computing device.

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