Rapid soft foundation consolidation degree deduction method based on depth operator digital intelligent model

Abstract

The invention relates to a depth operator digital intelligent model-based soft foundation consolidation degree rapid deduction method, which comprises the following steps of: obtaining soil layer thickness, layered structure, consolidation coefficient of each layer and drainage boundary condition of a soft soil foundation, and carrying out dimensionless processing on physical depth and physical time; generating a dimensionless consolidation coefficient field sample which changes along with the dimensionless depth, and dispersing the dimensionless consolidation coefficient field sample at a plurality of fixed depth positions; inputting the dimensionless time-depth coordinate into a backbone network of the physical information-depth operator network, inputting the consolidation coefficient discrete vector and the soil layer distribution parameter into a branch network of the physical information-depth operator network, and fusing the output of the backbone network and the output of the branch network to obtain an estimated value of the dimensionless hyperstatic pore water pressure; and training the physical information-depth operator network based on the physical information loss function to obtain a soft soil foundation consolidation prediction model. According to the method, rapid and accurate deduction of the consolidation process can be realized.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical mechanics and engineering technology, specifically relating to a method for rapid deduction of the degree of consolidation of soft foundation based on a depth operator numerical intelligent model. Background Technology

[0002] Soft soil foundations are widely used in roadbed filling, foundation treatment, and structural foundation design. Accurate and efficient prediction of their degree of consolidation is crucial for soft soil foundation design, construction control, and post-construction settlement assessment. The dissipation process of pore water pressure in natural soft soil is controlled by multiple factors, including drainage boundary conditions, soil layer distribution, and the spatial variability of the consolidation coefficient. Analytical solutions are typically only applicable under ideal conditions with simple soil layers and a uniform consolidation coefficient. In actual engineering, strata generally exhibit layered heterogeneous characteristics, with the consolidation coefficient varying significantly with depth and diverse drainage boundary combinations, often requiring approximate solutions using numerical methods. However, traditional numerical analysis is computationally expensive when repeatedly calculating under multiple conditions, and cannot meet real-time assessment needs, making it difficult to satisfy the requirements of rapid assessment, dynamic adjustment, and intelligent decision-making in soft soil foundation design and information-based construction. Currently, the commonly used methods for soft soil foundation consolidation analysis in engineering are the finite element method (FEM) and the finite difference method (FDM). These methods discretize the consolidation control equations spatially and temporally, constructing a mesh and constitutive model to solve for the spatiotemporal distribution of pore water pressure and degree of consolidation. For a given working condition, the results are relatively reliable. However, when drainage conditions, surcharge history, or filling height are frequently adjusted, repeated modeling and recalculation are often required, resulting in high modeling costs and computational overhead. When the consolidation coefficient exhibits a strongly non-uniform distribution or is characterized by a random field, the degrees of freedom increase dramatically, further reducing computational efficiency and making it difficult to meet the actual needs of multi-working-condition, rapid evaluation, and information-based construction.

[0003] With the development of artificial intelligence, data-driven models such as support vector machines, ensemble learning, convolutional neural networks, and recurrent neural networks have been introduced into soft foundation consolidation prediction. These models achieve rapid estimation of consolidation degree or settlement by learning the input-output relationship from historical data. However, these methods heavily rely on large-scale, high-quality samples, are sensitive to data distribution, and do not explicitly consider physical constraints such as consolidation control equations and drainage boundaries. Consequently, they are prone to insufficient prediction accuracy and limited generalization ability. Once the working conditions exceed the coverage of the training data, the model performance deteriorates significantly.

[0004] To compensate for the shortcomings of purely data-driven methods that are detached from physical mechanisms, Physical Information Neural Networks (PINNs) embed the residuals of partial differential governing equations and their initial / boundary conditions into the loss function. This allows for the simultaneous constraint of data errors and physical residuals during training, achieving some success in problems such as soft soil consolidation prediction and consolidation coefficient inversion. However, under multi-parameter conditions, long-term consolidation, and complex boundary conditions, PINNs are prone to training instability, slow convergence, and even convergence failure. Furthermore, they typically require separate training for different conditions, making it difficult to achieve "one-time training, multi-condition prediction."

[0005] DeepONet, based on the theory of universal operator approximation, treats solving partial differential equations as an "operator learning problem from the input function space to the solution function space." It encodes input functions (such as consolidation coefficient fields) through branch networks and time-space coordinates through the backbone network. Once the operator is trained, it can quickly infer from a large number of new input functions, achieving rapid prediction under multiple working conditions. Building upon this, DeepONet introduces residuals of governing equations and boundary condition constraints, further enhancing the physical consistency and generalization ability of operator predictions. Existing research has verified its feasibility in fluid mechanics, solid mechanics, and some geotechnical problems, but most studies are still limited to single drained boundaries or simplified consolidation coefficient distributions. When formation conditions or consolidation coefficient fields change, retraining or adjusting the network structure is usually necessary, making it difficult to simultaneously handle arbitrary drained boundaries and arbitrary consolidation coefficient fields within a unified framework.

[0006] Therefore, existing technologies lack a rapid deduction method for soft foundation consolidation that can simultaneously consider arbitrary drainage boundaries, complex layered structures, and spatial variability of consolidation coefficients in a unified model, while also taking into account prediction accuracy and computational efficiency. Summary of the Invention

[0007] To address the aforementioned problems in existing technologies, this invention provides a rapid method for extrapolating the consolidation degree of soft foundations based on a deep operator-based numerical intelligence model. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a method for rapid estimation of the consolidation degree of soft foundations based on a deep operator-based numerical intelligence model, comprising the following steps: The thickness of the soil layers, the layered structure, the consolidation coefficient of each layer, and the drainage boundary conditions of the soft soil foundation are obtained. The physical depth and physical time are processed to be dimensionless to obtain the dimensionless depth interval and the dimensionless time interval, and to form the dimensionless time-depth coordinate. A dimensionless consolidation coefficient field sample that varies with the dimensionless depth is generated in the dimensionless depth range, and the dimensionless consolidation coefficient field sample is discretized at several fixed depth positions to form a consolidation coefficient discrete vector. The dimensionless time-depth coordinates are input into the backbone network of the physical information-depth operator network, the consolidation coefficient discrete vector and soil layer distribution parameters are input into the branch network of the physical information-depth operator network, and the outputs of the backbone network and the branch network are fused to obtain the estimated value of the dimensionless excess pore water pressure. A consolidation prediction model for soft soil foundations is obtained by training a physical information-deep operator network based on a physical information loss function. The physical information loss function is constructed based on a one-dimensional consolidation control equation, initial conditions, and drainage boundary conditions. The consolidation prediction model for soft soil foundations is used to predict the excess pore water pressure field based on the dimensionless consolidation coefficient field, drainage boundary conditions, and soil layer distribution parameters of the target project.

[0008] In one embodiment of the present invention, the physical depth and physical time are dimensionless to obtain a dimensionless depth interval and a dimensionless time interval, forming a dimensionless time-depth coordinate system, including: The physical depth and physical time were dimensionlessly processed using the total soil layer thickness and characteristic consolidation duration to obtain dimensionless depth and dimensionless time intervals:

[0009] in, For dimensionless depth, For dimensionless time, The dimensionless excess pore water pressure For physical depth, For physical time, In physical depth With physical time The physical excess pore water pressure below The total thickness of the characteristic soil layer, For characteristic consolidation duration, The characteristic is the excess pore water pressure.

[0010] In one embodiment of the present invention, a dimensionless consolidation coefficient field that varies with the dimensionless depth is generated in the dimensionless depth range, and the dimensionless consolidation coefficient field is discretized at several fixed depth positions to form a consolidation coefficient discrete vector, including: Selecting the dimensionless depth range Discrete depth points Define a Gaussian random vector :

[0011] in, dimensionless depth A Gaussian random variable at the location; The Gaussian random vector covariance matrix for:

[0012] in, Standard deviation For the relevant length, This is an element-wise exponentiation operation; For the covariance matrix Perform Cholesky decomposition and introduce the Gaussian random vector. Define the dimensionless consolidation coefficient field sample at discrete points as:

[0013] in, Gaussian random vector The mean vector, It is a lower triangular matrix. A random vector that follows a multivariate standard normal distribution ; A discrete vector of consolidation coefficients is formed based on the dimensionless consolidation coefficient field samples at the discrete points. .

[0014] In one embodiment of the present invention, the physical information-deep operator network includes a backbone network, branch networks, and an output layer, wherein, The input to the backbone network is dimensionless time. Depth coordinates Output the backbone feature vector ; The input to the branch network is a discrete vector of the consolidation coefficient. The soil layer distribution parameters are used to output a branched feature vector. ; The output layer performs an inner product operation on the main feature vector and the branch feature vector to obtain an estimate of the dimensionless excess pore water pressure.

[0015] in, For physical information - deep operator networks in the consolidation coefficient field The following is an estimate of the dimensionless excess pore water pressure. For vectors , Dimensions For the dimensionless consolidation coefficient field.

[0016] In one embodiment of the present invention, both the backbone network and the branch network adopt a multi-layer feedforward fully connected structure. The multi-layer feedforward fully connected structure includes an input layer, several hidden layers and an output layer, and the activation function of each hidden layer is ReLU or tanh.

[0017] In one embodiment of the present invention, the backbone network has 6 hidden layers, each containing 60 neurons; The branch network has 5 hidden layers, each containing 60 neurons.

[0018] In one embodiment of the present invention, the soil layer distribution parameters of the branch network of the physical information-depth operator network include: permeability coefficient and volume compressibility coefficient.

[0019] In one embodiment of the present invention, the dimensionless form of the one-dimensional consolidation governing equation is as follows:

[0020] in, The dimensionless excess pore water pressure For dimensionless depth, For dimensionless time, The coefficient is dimensionless. , The total thickness of the characteristic soil layer, For characteristic consolidation duration, This is a sample of the dimensionless consolidation coefficient field; The initial conditions are:

[0021] in, The distribution of excess pore water pressure along depth at the initial loading moment; The drainage boundary conditions include top single-sided drainage and top and bottom double-sided drainage; The boundary conditions for top single-sided drainage are:

[0022]

[0023] The boundary conditions for top and bottom double-sided drainage are: 。

[0024] In one embodiment of the present invention, the physical information loss function is:

[0025] in, For the total loss function, For partial differential equation loss function, The initial conditional loss function, The boundary condition loss function; These are the non-negative weighting coefficients for each loss term; The partial differential equation loss function Represented as:

[0026] in, The number of combinatorial points for the partial differential equation. The first The dimensionless depth and dimensionless time of a partial differential equation paired with a point For physical information - deep operator networks in the consolidation coefficient field The following is an estimate of the dimensionless excess pore water pressure. For the dimensionless time partial derivative, The second partial derivative with respect to the dimensionless depth, The coefficient is dimensionless. The initial condition loss function Represented as:

[0027] In the formula, The number of initial condition matching points. For the first The dimensionless depth of the initial condition pairing point This represents the initial dimensionless excess pore water pressure at that depth. The boundary condition loss function The expression is:

[0028] in, The top boundary loss function is... The bottom boundary loss function; Top single-sided drainage boundary condition Below, top boundary loss function for:

[0029] in, The number of matching points at the top boundary. For the first Dimensionless time at the top boundary point; Top and bottom double-sided drainage boundary At that time, the bottom boundary loss function for:

[0030] Top single-sided drainage boundary condition At that time, the bottom boundary loss function for:

[0031] in, The number of points to match the bottom boundary. For the first Dimensionless time at the bottom boundary pairing point.

[0032] In one embodiment of the present invention, a physical information-deep operator network is trained based on a physical information loss function to obtain a soft soil foundation consolidation prediction model, including: The Adam optimizer is used to update the parameters of the physical information-deep operator network, with an initial learning rate of 100%. According to the inverse time decay strategy with decay rate The learning rate is dynamically adjusted, the number of training iterations is 10,000, the batch size is 32, and the ratio of training set to test set samples is 8:2, so that the physical information loss function is gradually reduced, and a soft soil foundation consolidation prediction model is obtained.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention presents a rapid deduction method for the degree of consolidation of soft soil foundations based on a depth operator-based intelligent model. A physical information-depth operator network is constructed on the basis of one-dimensional consolidation theory. Working condition information such as the consolidation coefficient field, drainage boundary conditions, and soil layer distribution parameters are input into the branch networks of the physical information-depth operator network, while time-depth coordinates are input into the backbone network. A physical information loss function is constructed by introducing one-dimensional consolidation control equations, initial conditions, and drainage boundary conditions for unified training. After training, for any combination of drainage boundaries, complex layered structures, and different spatial distributions of consolidation coefficients, only the corresponding consolidation coefficient field, drainage boundary conditions, and soil layer distribution parameters need to be input to quickly obtain the evolution of pore water pressure and the degree of consolidation over the entire time and at all depths. This achieves rapid deduction of soft soil foundation consolidation with "one-time training and multi-condition prediction," solving the problem in existing technologies where it is difficult to balance prediction accuracy and computational efficiency under arbitrary drainage boundaries, complex layered structures, and spatial variability of consolidation coefficients. This method enables rapid and accurate deduction of the consolidation process. Attached Figure Description

[0034] Figure 1 A flowchart illustrating a method for rapid deduction of the consolidation degree of soft foundation based on a deep operator numerical intelligence model, provided for an embodiment of the present invention; Figure 2A flowchart illustrating another method for rapid deduction of the consolidation degree of soft foundation based on a deep operator numerical intelligence model provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a multi-layered soil consolidation model; Figure 4 A schematic diagram showing the pore pressure prediction results of a single soil layer under double-sided and top drainage conditions with different consolidation coefficients in TDC-PI-DeepONet. Figure 5 A schematic diagram showing the pore pressure prediction results of two-layer soil under double-sided and top drainage conditions with different consolidation coefficients in TDC-PI-DeepONet. Figure 6 This is a schematic diagram of the TDC-PI-DeepONet pore pressure prediction results under the random consolidation coefficient field of TDC-PI-DeepONet. Detailed Implementation

[0035] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0036] Example 1 This embodiment addresses the challenges in design calculations and information-based construction process control for soft soil foundation engineering, particularly the issues of lengthy numerical solutions, repeated modeling, insufficient generalization ability, and difficulty in ensuring physical consistency under complex working conditions. These problems lead to difficulties in rapidly assessing the consolidation response. The embodiment provides a method for rapidly extrapolating the degree of consolidation of soft soil foundations based on a deep operator-based digital intelligent model. This method can be applied to soft soil foundations under any geological conditions, considering their layered structure, spatial variability of consolidation coefficients, and diverse drainage boundary forms.

[0037] Please see Figure 1 and Figure 2 , Figure 1 This is a flowchart illustrating a method for rapid deduction of the consolidation degree of soft foundations based on a deep operator numerical intelligence model, provided in an embodiment of the present invention. Figure 2 A flowchart illustrating another method for rapid deduction of the consolidation degree of soft foundation based on a deep operator numerical intelligence model, provided in an embodiment of the present invention.

[0038] This embodiment of the method for rapid deduction of the consolidation degree of soft foundation based on the deep operator numerical intelligence model includes the following steps: S1. Obtain the soil layer thickness, layer structure, consolidation coefficient of each layer, and drainage boundary conditions of the soft soil foundation. Perform dimensionless processing on the physical depth and physical time to obtain dimensionless depth intervals and dimensionless time intervals, and form dimensionless time-depth coordinates.

[0039] Specifically, by utilizing geological survey and design data, the thickness, elevation range, layer structure, consolidation coefficient range of each layer, and drainage boundary conditions of the soft soil foundation are determined. From these conditions, the physical depth can be obtained. Physical time and in physical depth With physical time Physical excess pore water pressure .

[0040] The physical depth and physical time were dimensionlessly processed using the total soil layer thickness and characteristic consolidation duration to obtain dimensionless depth and dimensionless time intervals:

[0041] in, For the dimensionless depth range, For a dimensionless time interval, The dimensionless excess pore water pressure For physical depth, For physical time, In physical depth With physical time The physical excess pore water pressure below The total thickness of the characteristic soil layer, For characteristic consolidation duration, The characteristic is the excess pore water pressure.

[0042] For example, setting the characteristic consolidation duration Total thickness of characteristic soil layers The normalized amplitude of the initial excess pore water pressure is the characteristic excess pore water pressure. .

[0043] Furthermore, dimensionless time-depth coordinates are formed based on dimensionless depth intervals and dimensionless time intervals. .

[0044] S2. Generate a dimensionless consolidation coefficient field sample that varies with the dimensionless depth in the dimensionless depth range, and discretize the dimensionless consolidation coefficient field sample at several fixed depth positions to form a consolidation coefficient discrete vector.

[0045] To characterize the spatial variability of the consolidation coefficient field, a log-normal Gaussian random field is constructed for the consolidation coefficient field. As a multi-condition training sample set, it is input into the physical information-deep operator network, and further, to facilitate neural network processing, In the depth range Discretized into vectors The specific steps include: First, in the dimensionless depth range Select Discrete depth points Define a Gaussian random vector .

[0046] Specifically, in the dimensionless depth range Select Discrete depth points (sensor points):

[0047] in, , can be:

[0048] At discrete points Based on this, Gaussian random vectors are generated using Gaussian random fields (GRF). For example, the length scale parameter is selected as... A Gaussian random field generator produces a set of Gaussian random vectors. :

[0049] Then, a log-normal random field generation method based on Cholesky decomposition is used to construct... For example, suppose the logarithmic field (i.e., Gaussian random vectors) is... Random fields satisfy:

[0050] in, Gaussian random vector The mean of Y(z), Gaussian random vector The point standard deviation of Y(z).

[0051] Given mean with standard deviation Let the coefficient of variation be:

[0052] Then it is acceptable:

[0053]

[0054] Furthermore, an exponential covariance function is used to construct the logarithmic field covariance matrix. :

[0055] in, Standard deviation For the relevant length, This is for element-wise exponentiation.

[0056] For covariance matrix Performing Cholesky decomposition, we obtain:

[0057] in, It is a lower triangular matrix.

[0058] Generate random vectors that follow a multivariate standard normal distribution. , It is a zero vector. Given the identity matrix, construct the Gaussian random vector as follows:

[0059] in, Gaussian random vector The mean vector.

[0060] The dimensionless consolidation coefficient at discrete points is then defined as:

[0061] in, It is a vector consisting entirely of 1s.

[0062] For example, the above parameters can be taken as: mean Standard deviation Relevant length Number of discrete points .

[0063] Therefore, a discrete vector of consolidation coefficients is formed based on the dimensionless consolidation coefficient field samples at discrete points. Multiple sets of consolidation coefficient field samples with different spatial variation characteristics were obtained and used to uniformly train the consolidation prediction operator for soft soil foundation.

[0064] Furthermore, based on steps S1 and S2, in the dimensionless spatiotemporal domain The internal structure is as follows: (1) Matching point set: , representing time-depth coordinates; (2) Initial point set: , indicates the initial conditions; (3) Boundary point set: and Indicates drainage boundary conditions; (4) Test point set: .

[0065] For example, , , , , .

[0066] S3. Input the dimensionless time-depth coordinates into the backbone network of the physical information-depth operator network, input the consolidation coefficient discrete vector and soil layer distribution parameters into the branch network of the physical information-depth operator network, and fuse the outputs of the backbone network and the branch network to obtain the estimated value of the dimensionless excess pore water pressure.

[0067] Please see Figure 2 The Physical Information-Deep Operator Network (TDC-PI-DeepONet) consists of a backbone network, branch networks, and an output layer.

[0068] The backbone network is fed into dimensionless time-depth coordinates. That is, by combining the point set, the main feature vector is output. The input to the branch network is a discrete vector of consolidation coefficients. The soil layer distribution parameters are used to output a branched feature vector. The output layer performs an inner product operation on the main feature vector and the branch feature vectors to obtain an estimate of the dimensionless excess pore water pressure.

[0069] in, For physical information - deep operator networks in the consolidation coefficient field The following is an estimate of the dimensionless excess pore water pressure. For vectors , Dimensions For the dimensionless consolidation coefficient field.

[0070] Specifically, both the backbone and branch networks employ a multi-layer feedforward fully connected structure. This structure includes an input layer, several hidden layers, and an output layer. The activation function for each hidden layer is ReLU or tanh. The number of hidden layers in both the backbone and branch networks is the same as or similar to the number of neurons. Network parameters are initialized using the Xavier method (also known as Glorotnormal). For example, the backbone network has 6 hidden layers, each containing 60 neurons; the branch network has 5 hidden layers, each containing 60 neurons.

[0071] For example, the random seed is set to 12345; the branch network layer structure can be set to [100,60,60,60,60,60]; the backbone network layer structure can be set to [2,60,60,60,60,60]; the activation function is tanh, and the network parameter initialization method is Glorot normal.

[0072] Please see Figure 3 , Figure 3 This is a schematic diagram of a multi-layered soil consolidation model, except for the discrete vector of the consolidation coefficient. The soil layer distribution parameters of the branch network of the input physical information-depth operator network include: the permeability coefficient of each soil layer. and volume compressibility ,in, This represents the number of soil layers.

[0073] S4. The physical information-deep operator network is trained based on the physical information loss function to obtain the consolidation prediction model for soft soil foundation.

[0074] Specifically, the consolidation coefficient is discretized into a vector. Input the soil layer distribution parameters into the branch network, and match the point coordinates. The excess pore water pressure is estimated by inputting it into the backbone network during the forward propagation process, thus obtaining the estimated value of the excess pore water pressure. Secondly, according to The physical information loss function is calculated to obtain its residual. Then, based on the residual, the weights and biases of the branch network and the backbone network are continuously updated in reverse using the chain rule to gradually reduce the physical information loss function, thus obtaining the predictive operator for the spatiotemporal response of the consolidation coefficient function field to the pore pressure.

[0075] The physical information loss function is constructed based on the one-dimensional consolidation governing equations, initial conditions, and drained boundary conditions. It includes a partial differential equation loss function (i.e., the governing equation loss function), an initial condition loss function, and a boundary condition loss function. The partial differential equation loss function is constructed based on the sum of squares of the residuals of the consolidation governing equations at each combination point of the partial differential equations. The initial condition loss function is constructed based on the square of the difference between the predicted value at the initial time and the initial pore pressure distribution. The boundary condition loss function is constructed based on the square of the residuals of the predicted value or normal derivative at the drained or undrained boundary.

[0076] Specifically, the physical dimension form of the one-dimensional consolidation governing equation for soft soil is as follows:

[0077] in, For physical space depth With physical time The pressure of the superstatic pore water below The physical consolidation coefficient varies with depth.

[0078] Define dimensionless coefficients :

[0079] in, The total thickness of the characteristic soil layer, For characteristic consolidation duration, For example, , , .

[0080] The dimensionless form of the one-dimensional consolidation governing equation is:

[0081] in, The dimensionless excess pore water pressure For dimensionless depth, For dimensionless time, The coefficient is dimensionless. , The total thickness of the characteristic soil layer, For characteristic consolidation duration, This is a sample of the dimensionless consolidation coefficient field.

[0082] The initial conditions are:

[0083] in, The distribution of excess pore water pressure along depth at the initial loading moment.

[0084] Drainage boundary conditions include top single-sided drainage and top and bottom double-sided drainage; The boundary conditions for top single-sided drainage are:

[0085]

[0086] in, Indicates top drainage. This indicates that the bottom does not drain.

[0087] The boundary conditions for top and bottom double-sided drainage are: 。

[0088] The physical information loss function is expressed as:

[0089] in, For the total loss function, For partial differential equation loss function, The initial conditional loss function, The boundary condition loss function; These are the non-negative weighting coefficients for each loss term.

[0090] A partial differential equation loss function is constructed using the dimensionless form of the one-dimensional consolidation governing equation. , is represented as:

[0091] in, The number of combinatorial points for the partial differential equation. The first The dimensionless depth and dimensionless time of a partial differential equation paired with a point Indicates the first One matching point, For physical information - deep operator networks in the consolidation coefficient field The following is an estimate of the dimensionless excess pore water pressure. For the dimensionless time partial derivative, The second partial derivative with respect to the dimensionless depth, This is a dimensionless coefficient. For example, Set it to 10000.

[0092] Initial condition loss function Related to the initial pore pressure, it can be expressed as:

[0093] In the formula, The number of initial condition matching points. For the first The dimensionless depth of the initial condition pairing point This represents the initial dimensionless excess pore water pressure at that depth. For example, Set to 1000, .

[0094] Boundary condition loss functions include the top boundary loss function. and bottom boundary loss function , and Used to constrain pore pressure at boundary points. Boundary condition loss function. The expression is:

[0095] Top single-sided drainage boundary condition Below, top boundary loss function for:

[0096] in, The number of matching points at the top boundary. For the first Dimensionless time at the top boundary point; Top and bottom double-sided drainage boundary At that time, the bottom boundary loss function for:

[0097] Top single-sided drainage boundary condition At that time, the bottom boundary loss function for:

[0098] in, The number of points to match the bottom boundary. For the first The dimensionless time of the bottom boundary pairing point. For example, , The number is set to 1000.

[0099] Correspondingly, the physical information loss function can be expressed as:

[0100] For example, it is advisable =[1,10,100,100].

[0101] Furthermore, the Adam optimizer is used to update the parameters of the physical information-deep operator network, with an initial learning rate of [value missing]. According to the inverse time decay strategy with decay rate The learning rate was dynamically adjusted, the number of training iterations was 10,000, the batch size was 32, and the ratio of training set to test set samples was approximately 8:2, so that the physical information loss function was gradually reduced, and a consolidation prediction model for soft soil foundation was obtained.

[0102] It should be noted that when the physical information loss function When a predetermined standard is met or a predetermined number of training iterations are reached, training is completed and a pore pressure prediction operator is obtained. It should be noted that the predetermined standard can be set according to actual conditions, and this embodiment does not impose specific limitations on it.

[0103] Furthermore, the trained soft soil foundation consolidation prediction model is used to predict the excess pore water pressure field based on the dimensionless consolidation coefficient field, drainage boundary conditions, and soil layer distribution parameters of the target project. This prediction model can also predict any new dimensionless consolidation coefficient field. The drainage boundary form and soil layer structure are input into the trained soft soil foundation consolidation prediction model to obtain the dimensionless excess pore water pressure field at any dimensionless time and any dimensionless depth. This enables rapid prediction of the consolidation process of soft soil foundations under arbitrary drainage boundaries and strata conditions.

[0104] Specifically, the consolidation coefficient function field under the working condition to be predicted With test point set Input the trained TDC-PI-DeepONet model, and it will output directly. This allows for a rapid deduction of the pore pressure dissipation process. Furthermore, the test point set can be... This embodiment does not specifically limit whether sampling is uniform in the spatiotemporal domain or denser at locations of engineering interest.

[0105] Please see Figure 4 and Figure 5 , Figure 4 This is a schematic diagram showing the pore pressure prediction results of a single soil layer under two-sided and top drainage conditions with different consolidation coefficients using TDC-PI-DeepONet. Figure 4 (a), (b), and (c) in the text correspond to respectively The model is used to predict the spatiotemporal evolution of normalized excess pore pressure u / u0 under two-sided drainage / top drainage conditions, with three operating conditions: 0.1, 0.2, and 0.5. The prediction curves are highly consistent with the analytical solutions under different time scales and two types of drainage boundaries, indicating that TDC-PI-DeepONet can maintain high accuracy and high inference efficiency under complex operating conditions. Figure 5 This is a schematic diagram showing the pore pressure prediction results of a two-layer soil under double-sided and top drainage conditions with different consolidation coefficients in TDC-PI-DeepONet. Figure 5 (a), (b), and (c) in the figure correspond to three sets of double-layered consolidation coefficients (c v1 c v2 Operating conditions, layered on the left. The input shows the spatiotemporal evolution prediction of normalized pore pressure u / u0 under double-sided drainage and top drainage. The right side compares the analytical solutions of profiles at different times. The results show that even under the conditions of stratification leading to interface inflection points and heterogeneous diffusion, TDC-PI-DeepONet still maintains high consistency with the analytical solution, demonstrating strong generalization ability and rapid inference advantages. Figure 4 and Figure 5 TDC-PI-DeepONet demonstrates high overall prediction accuracy in single-layer consolidation problems, across all operating conditions. The relative errors were all maintained at Within the order of magnitude; the overall error level of the prediction results for two-layer soil is less than 3%, with the error controlled within 1.5% in the case of double-sided drainage. The benchmark solution is... The predicted solution is There are a total of discrete evaluation points The nth sample point is denoted as the nth sample point. The baseline and predicted values ​​for each point are respectively , ,but The formula for calculating relative error is: .

[0106] Please see Figure 6 , Figure 6 This is a schematic diagram of the TDC-PI-DeepONet pore pressure prediction results under a random consolidation coefficient field. The diagram uses a log-normal Gaussian random field to construct multiple sets of... The mean is 0.3, and only the standard deviation is changed. For each set of random consolidation coefficient fields, the pre-trained TDC-PI-DeepONet is directly called under both top drainage and top-bottom double-sided drainage conditions to obtain pore water pressure profiles at different consolidation times. Figure 6 It can be seen that TDC-PI-DeepONet has good predictive generalization ability for any consolidation coefficient field conditions.

[0107] In this embodiment, a rapid calculation method for the degree of consolidation of soft soil foundation based on a depth operator-based numerical model is constructed. A physical information-depth operator network is built upon one-dimensional consolidation theory. Working condition information such as the consolidation coefficient field, drainage boundary conditions, and soil layer distribution parameters are input into the branch networks of the physical information-depth operator network, while time-depth coordinates are input into the backbone network. A physical information loss function is constructed by introducing one-dimensional consolidation control equations, initial conditions, and drainage boundary conditions for unified training. After training, for any combination of drainage boundaries, complex layered structures, and different spatial distributions of consolidation coefficients, only the corresponding consolidation coefficient field, drainage boundary conditions, and soil layer distribution parameters need to be input to quickly obtain the dimensionless excess pore water pressure field over the entire duration and depth without further training. The evolution and consolidation degree distribution enable rapid simulation of soft soil consolidation under multiple working conditions through "one training session". This solves the problem in existing technologies where it is difficult to balance prediction accuracy and computational efficiency for soft soil foundations under conditions of arbitrary drainage boundaries, complex layered structures, and spatial variability of consolidation coefficients. It can achieve rapid and accurate simulation of the consolidation process.

[0108] The method described in this embodiment can be used for soft soil filling scheme comparison, stability assessment, and post-construction settlement prediction, supporting rapid updating and verification of key parameters. During the construction phase, it can be linked with on-site monitoring data to achieve rapid assessment and early warning of settlement and stability, thereby guiding the dynamic adjustment of construction parameters and the optimization of drainage and loading measures. This provides support for dynamic parameter adjustment and rapid decision-making in information-based construction, improving the safety, economy, and controllability of project implementation.

[0109] 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 method for rapid deduction of the consolidation degree of soft foundations based on a deep operator-based numerical intelligence model, characterized in that, Including the following steps: The thickness of the soil layers, the layered structure, the consolidation coefficient of each layer, and the drainage boundary conditions of the soft soil foundation are obtained. The physical depth and physical time are processed to be dimensionless to obtain the dimensionless depth interval and the dimensionless time interval, and to form the dimensionless time-depth coordinate. A dimensionless consolidation coefficient field sample that varies with the dimensionless depth is generated in the dimensionless depth range, and the dimensionless consolidation coefficient field sample is discretized at several fixed depth positions to form a consolidation coefficient discrete vector. The dimensionless time-depth coordinates are input into the backbone network of the physical information-depth operator network, the consolidation coefficient discrete vector and soil layer distribution parameters are input into the branch network of the physical information-depth operator network, and the outputs of the backbone network and the branch network are fused to obtain the estimated value of the dimensionless excess pore water pressure. A consolidation prediction model for soft soil foundations is obtained by training a physical information-deep operator network based on a physical information loss function. The physical information loss function is constructed based on a one-dimensional consolidation control equation, initial conditions, and drainage boundary conditions. The consolidation prediction model for soft soil foundations is used to predict the excess pore water pressure field based on the dimensionless consolidation coefficient field, drainage boundary conditions, and soil layer distribution parameters of the target project.

2. The method for rapid deduction of soft foundation consolidation degree based on deep operator numerical intelligence model according to claim 1, characterized in that, The physical depth and physical time are dimensionless to obtain dimensionless depth and time intervals, forming dimensionless time-depth coordinates, including: The physical depth and physical time were dimensionlessly processed using the total soil layer thickness and characteristic consolidation duration to obtain dimensionless depth and dimensionless time intervals: in, For dimensionless depth, For dimensionless time, The dimensionless excess pore water pressure For physical depth, For physical time, In physical depth With physical time The physical excess pore water pressure below The total thickness of the characteristic soil layer, For characteristic consolidation duration, The characteristic is the excess pore water pressure.

3. The method for rapid deduction of soft foundation consolidation degree based on deep operator numerical intelligence model according to claim 1, characterized in that, A dimensionless consolidation coefficient field that varies with the dimensionless depth is generated within the dimensionless depth range, and the dimensionless consolidation coefficient field is discretized at several fixed depth positions to form a consolidation coefficient discrete vector, including: Selecting the dimensionless depth range Discrete depth points Define a Gaussian random vector : in, dimensionless depth A Gaussian random variable at the location; The Gaussian random vector covariance matrix for: in, Standard deviation For the relevant length, This is an element-wise exponentiation operation; For the covariance matrix Perform Cholesky decomposition and introduce the Gaussian random vector. Define the dimensionless consolidation coefficient field sample at discrete points as: in, Gaussian random vector The mean vector, It is a lower triangular matrix. A random vector that follows a multivariate standard normal distribution ; A discrete vector of consolidation coefficients is formed based on the dimensionless consolidation coefficient field samples at the discrete points. .

4. The method for rapid deduction of soft foundation consolidation degree based on deep operator numerical intelligence model according to claim 3, characterized in that, The physical information-deep operator network includes a backbone network, branch networks, and an output layer, wherein... The input to the backbone network is dimensionless time-depth coordinates. Output the backbone feature vector ; The input to the branch network is a discrete vector of the consolidation coefficient. The soil layer distribution parameters are used to output a branched feature vector. ; The output layer performs an inner product operation on the main feature vector and the branch feature vector to obtain an estimate of the dimensionless excess pore water pressure. in, For physical information - deep operator networks in the consolidation coefficient field The following is an estimate of the dimensionless excess pore water pressure. For vectors , Dimensions For the dimensionless consolidation coefficient field.

5. The method for rapid deduction of the consolidation degree of soft foundation based on the deep operator numerical intelligence model according to claim 1, characterized in that, Both the backbone network and the branch network adopt a multi-layer feedforward fully connected structure. The multi-layer feedforward fully connected structure includes an input layer, several hidden layers, and an output layer. The activation function of each hidden layer is ReLU or tanh.

6. The method for rapid deduction of the consolidation degree of soft foundation based on the deep operator numerical intelligence model according to claim 5, characterized in that, The backbone network has 6 hidden layers, each containing 60 neurons; The branch network has 5 hidden layers, each containing 60 neurons.

7. The method for rapid deduction of the consolidation degree of soft foundation based on the deep operator numerical intelligence model according to claim 1, characterized in that, The soil layer distribution parameters of the branch network of the physical information-depth operator network include: permeability coefficient and volume compressibility coefficient.

8. The method for rapid deduction of the consolidation degree of soft foundation based on the deep operator numerical intelligence model according to claim 1, characterized in that, The dimensionless form of the one-dimensional consolidation governing equation is: in, The dimensionless excess pore water pressure For dimensionless depth, For dimensionless time, The coefficient is dimensionless. , The total thickness of the characteristic soil layer, For characteristic consolidation duration, This is a sample of the dimensionless consolidation coefficient field; The initial conditions are: in, The distribution of excess pore water pressure along depth at the initial loading moment; The drainage boundary conditions include top single-sided drainage and top and bottom double-sided drainage; The boundary conditions for top single-sided drainage are: The boundary conditions for top and bottom double-sided drainage are: 。 9. The method for rapid deduction of the consolidation degree of soft foundation based on the deep operator numerical intelligence model according to claim 8, characterized in that, The physical information loss function is: in, For the total loss function, For partial differential equation loss function, The initial conditional loss function, The boundary condition loss function; These are the non-negative weighting coefficients for each loss term; The partial differential equation loss function Represented as: in, The number of combinatorial points for the partial differential equation. The first The dimensionless depth and dimensionless time of a partial differential equation paired with a point For physical information - deep operator networks in the consolidation coefficient field The following is an estimate of the dimensionless excess pore water pressure. For the dimensionless time partial derivative, The second partial derivative with respect to the dimensionless depth, The coefficient is dimensionless. The initial condition loss function Represented as: In the formula, The number of initial condition matching points. For the first The dimensionless depth of the initial condition pairing point This represents the initial dimensionless excess pore water pressure at that depth. The boundary condition loss function The expression is: in, The top boundary loss function is... The bottom boundary loss function; Top single-sided drainage boundary condition Below, top boundary loss function for: in, The number of matching points at the top boundary. For the first Dimensionless time at the top boundary point; Top and bottom double-sided drainage boundary At that time, the bottom boundary loss function for: Top single-sided drainage boundary condition At that time, the bottom boundary loss function for: in, The number of points to match the bottom boundary. For the first Dimensionless time at the bottom boundary pairing point.

10. The method for rapid deduction of the consolidation degree of soft foundation based on the deep operator numerical intelligence model according to claim 1, characterized in that, A physical information-deep operator network is trained based on the physical information loss function to obtain a soft soil foundation consolidation prediction model, including: The Adam optimizer is used to update the parameters of the physical information-deep operator network, with an initial learning rate of 100%. According to the inverse time decay strategy with decay rate The learning rate is dynamically adjusted, the number of training iterations is 10,000, the batch size is 32, and the ratio of training set to test set samples is 8:2, so that the physical information loss function is gradually reduced, and a soft soil foundation consolidation prediction model is obtained.

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