A tunnel surrounding rock lining coupling analysis method, system, electronic device and storage medium

Abstract

The application relates to the field of tunnel engineering intelligent monitoring, in particular to a tunnel surrounding rock lining coupling analysis method and system, an electronic device and a storage medium, which comprises the following steps: a neural network containing an input layer, a hidden layer and a physical constraint layer is established, a displacement discontinuity condition, a stress balance condition and a seepage continuity condition are forced to be met at a lining joint position through a Lagrange multiplier network, and a joint damage evolution and a seepage-stress-temperature-damage four-field coupling process are embedded into a loss function; dominant space modes of the four-field coupling are extracted through intrinsic orthogonal decomposition, a mapping relationship from input parameters to mode coefficients is established in combination with Gaussian process regression, and an intrinsic orthogonal decomposition-Gaussian process reduced-order surrogate model is constructed; real-time prediction is realized; and the problems that a traditional physical information neural network cannot strictly meet physical conservation laws of normal contact at a joint, stress balance and seepage continuity, leading to large joint damage simulation error and poor convergence are solved.

Description

Technical Field

[0001] This invention relates to the field of intelligent monitoring of tunnel engineering, specifically a method, system, electronic device, and storage medium for coupled analysis of tunnel surrounding rock lining. Background Technology

[0002] During service, tunnel surrounding rock and lining structures experience multi-field coupling effects of seepage, stress, temperature, and damage. As weak points in the structure, lining joints are prone to widening, increased leakage, and damage evolution, directly impacting the overall stability and operational safety of the tunnel. Therefore, accurate simulation and real-time prediction of the rock-lining coupling effect are core technologies for tunnel safety management.

[0003] Existing technologies are mainly divided into two categories: The first category is full-order finite element / finite difference simulation methods based on numerical software such as FLAC3D and ABAQUS. These methods involve dense mesh generation and large iterative computations, with a single full-scale calculation taking several hours, failing to meet the millisecond-level real-time early warning and rapid decision-making requirements in tunnel operations. The second category is data-driven prediction methods based on deep learning such as LSTM and GRU. These methods are computationally fast, but the models rely entirely on monitoring data for training, without embedding physical conservation equations and structural mechanics constraints. In scenarios with missing monitoring data or extreme condition extrapolation, the prediction accuracy drops sharply, resulting in insufficient engineering reliability.

[0004] Tunnel lining joints exhibit strong nonlinear characteristics, including displacement discontinuities, stress discontinuities, and abrupt changes in seepage channels. Traditional physical information neural networks, employing soft constraints based on loss functions, cannot strictly satisfy the physical conservation laws governing normal contact, stress balance, and seepage continuity at the joints, leading to large simulation errors and poor convergence in joint damage simulation. Furthermore, the computational burden of solving the entire spatial field is substantial, making real-time inference at the edge difficult. Summary of the Invention

[0005] In order to solve the problems existing in the prior art, the present invention provides a method, system, electronic device and storage medium for coupled analysis of tunnel surrounding rock lining.

[0006] This invention is achieved using the following technical solution: A coupled analysis method for tunnel surrounding rock lining includes the following steps: A hard-constrained physical information neural network is constructed, which includes an input layer, a hidden layer, and a physical constraint layer. At the lining joint, the displacement discontinuity condition, stress equilibrium condition, and seepage continuity condition are forced to be satisfied through a Lagrange multiplier network. The joint damage evolution and the four-field coupling process of seepage-stress-temperature-damage are embedded in the loss function. A reduced-order model is established by extracting the four-field coupled dominant spatial modes through intrinsic orthogonal decomposition and establishing the mapping relationship between input parameters and mode coefficients by combining Gaussian process regression, thus constructing an intrinsic orthogonal decomposition-Gaussian process reduced-order surrogate model. Real-time prediction involves deploying the hard-constrained physical information neural network on edge computing nodes, inverting the state of the surrounding rock and lining structure based on monitoring data, and inputting the inverted parameters into the reduced-order model to predict the evolution of the surrounding rock-lining coupled field.

[0007] Furthermore, the displacement discontinuity condition is as follows: the joint normal gap is less than or equal to zero, the normal Lagrange multiplier is greater than or equal to zero, and the product of the normal Lagrange multiplier and the joint normal gap is zero. The augmented Lagrange method is used to iteratively update the normal Lagrange multiplier. The update rule is as follows: add the current normal Lagrange multiplier to the product of the penalty parameter and the current normal gap, compare the sum with zero, and take the larger value as the updated normal Lagrange multiplier. The joint normal gap is obtained by subtracting the joint opening from the projection of the displacement vector difference on both sides of the joint onto the joint normal unit vector.

[0008] Furthermore, the seepage continuity condition satisfies the coupling change of the permeability coefficient with the joint damage variable: the permeability coefficient is equal to the intact permeability coefficient, plus the difference between the fully damaged permeability coefficient and the intact permeability coefficient, and then multiplied by a specified exponent power of the joint damage variable; the specified exponent is the damage-permeability coupling exponent, with a value range of 2-4.

[0009] Furthermore, the loss function is obtained by adding three parts: the data fitting term, the first weight multiplied by the physical residual term, and the second weight multiplied by the boundary condition term; wherein, the first weight is the physical constraint weight, the second weight is the boundary constraint weight, and the second weight is 10-100 times the first weight.

[0010] Furthermore, the intrinsic orthogonal decomposition selects the first ten to thirtieth modes with a cumulative energy percentage greater than 99%.

[0011] Furthermore, it also includes federated learning collaborative optimization steps, including: Each tunnel locally trains the hard-constraint physical information neural network and calculates the physical parameter sensitivity matrix; The cloud platform calculates weighted aggregation weights based on geological condition similarity, physical behavior similarity, and local model accuracy, and then aggregates the models. Differential privacy processing is used before parameters are uploaded, and the original data is saved locally.

[0012] Furthermore, the aggregation weight is obtained by weighted summation of three parts: the first coefficient multiplied by the cosine similarity of geological conditions, the second coefficient multiplied by the reciprocal of the Euclidean distance of the physical parameter sensitivity matrix, and the third coefficient multiplied by the accuracy of the local model; wherein, the first coefficient, the second coefficient, and the third coefficient are preset normalization coefficients, all of which are positive numbers and the sum of the three is 1.

[0013] A coupled analysis system for tunnel surrounding rock lining, employing the method described in this invention, includes: The neural network construction module is used to establish a hard-constrained physical information neural network containing an input layer, a hidden layer, and a physical constraint layer. The physical constraint layer is set at the lining joint, and the displacement discontinuity condition, stress balance condition, and seepage continuity condition are forcibly satisfied through a parallel Lagrange multiplier network. The joint damage evolution and the four-field coupling process of seepage-stress-temperature-damage are embedded in the loss function. The reduced-order model building module is used to extract the four-field coupled dominant spatial modes through intrinsic orthogonal decomposition, and to establish the mapping relationship between input parameters and mode coefficients by combining Gaussian process regression, thereby constructing an intrinsic orthogonal decomposition-Gaussian process reduced-order surrogate model. The real-time prediction module is used to deploy a hard-constrained physical information neural network on edge computing nodes, invert the state of the surrounding rock and lining structure based on monitoring data, input the inversion parameters into a reduced-order model, and predict the evolution of the surrounding rock-lining coupled field.

[0014] An electronic device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method as described in this invention.

[0015] A computer-readable storage medium having a computer program stored thereon for causing a computer to perform the methods described in this invention.

[0016] This invention provides a method, system, electronic device, and storage medium for coupled analysis of tunnel surrounding rock lining, which has the following advantages compared with the prior art: 1. This method introduces a Lagrange multiplier network at the lining joint location, directly embedding the displacement discontinuity condition, stress equilibrium condition, and seepage continuity condition as hard constraints into the neural network architecture, rather than indirectly constraining them through the loss function penalty term. This significantly improves the accuracy of the contact condition satisfaction. Experiments show that the joint normal gap violation rate of the traditional soft constraint PINN is about 3%, while the hard constraint scheme of this invention can reduce this index to below 0.01%, reaching the machine accuracy level, and effectively solving the numerical stability problem of joint contact analysis.

[0017] 2. This method adopts an architecture design that cascades a hard-constrained physical information neural network and a reduced-order model. The edge computing nodes only run a lightweight neural network inversion module, while the complex field prediction is completed by the reduced-order model. This division of tasks keeps the single inference time of the edge computing nodes within 100 milliseconds, while ensuring prediction accuracy. It meets the timeliness requirements of real-time safety monitoring during tunnel operation and resolves the contradiction between the limited computing power of edge devices and the complexity of the model.

[0018] 3. This method introduces a physical parameter sensitivity matrix as a similarity measure in the federated learning framework, so that the model aggregation weights not only consider the statistical characteristics of the data, but also take into account the characteristics of geotechnical mechanical behavior. Compared with the traditional federated averaging algorithm, the physical perception aggregation strategy of this invention effectively improves the model accuracy of new tunnels when monitoring data is limited, and does not require uploading the original monitoring data, effectively protecting data privacy and solving the knowledge transfer problem in collaborative modeling of tunnel groups. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention.

[0020] Figure 2 This is a system structure block diagram of the present invention.

[0021] Figure 3 This is a block diagram of the electronic device structure of the present invention. Detailed Implementation

[0022] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0023] The following description, with reference to the accompanying drawings, outlines a method, system, electronic device, and storage medium for coupled analysis of tunnel surrounding rock lining according to embodiments of the present invention.

[0024] Specifically, Figure 1 This is a schematic flowchart of a coupling analysis method for tunnel surrounding rock lining provided in an embodiment of the present invention.

[0025] To clearly describe this solution, the following technical features are defined using terminology: Damage-permeability coupling index: a nonlinear amplification factor of joint damage variable on permeability coefficient, with a value range of 2-4; First weight: The weighting coefficient of the physical residual term in the loss function, with a value ranging from 0.1 to 1.0; Second weight: The weight coefficient of the boundary condition term in the loss function, which is 10-100 times that of the first weight; Preset normalization coefficients: The allocation coefficients for cloud aggregation weights are all positive numbers and the sum of the three is 1.

[0026] like Figure 1 As shown, the coupled analysis method for tunnel surrounding rock lining includes the following steps: S1: Constructing a hard-constraint physical information neural network The hard-constraint physical information neural network is a physical information neural network that embeds a Lagrange multiplier network and a dedicated physical constraint layer. Through forced constraints at the network architecture level, it ensures that the lining joint location strictly meets the displacement discontinuity condition, stress equilibrium condition, and seepage continuity condition. Furthermore, the joint damage evolution and the four-field coupling control equations of seepage-stress-temperature-damage are directly embedded into the network loss function for training, thereby achieving high-precision and high-stability simulation of the strongly nonlinear discontinuous behavior of the joint. A deep neural network containing an input layer, hidden layers, and a physical constraint layer is established. The input layer receives spatiotemporal coordinate information, surrounding rock and lining material parameters, and boundary condition parameters. The hidden layer adopts a fully connected structure, with an optimal number of layers (8 to 12) and 64 to 128 neurons per layer. The activation function uses the hyperbolic tangent function or the Swish function, which is superior in terms of continuity and differentiability, gradient smoothness, and physical field continuity constraints, reducing spurious solutions for abrupt changes in stress and seepage fields and improving the convergence speed of physical constraints. The four-field coupling is a strongly nonlinear problem; too few layers cannot fit the high-dimensional nonlinear mapping, while too many layers easily lead to gradient vanishing and overfitting. 8-12 layers achieve an optimal balance between fitting capability and training stability. The input dimensions are spatiotemporal coordinates + material parameters + boundary conditions (7-15 dimensions in total), and the outputs are displacement, stress, permeability, temperature, and damage (12 dimensions in total). The 64-128 dimensional hidden layer space can fully preserve the physical field characteristics while avoiding redundant computation. The joint constraint penalty parameter is set to 10³-10⁶, ensuring that the normal gap violation rate is below 0.01%.

[0027] A physical constraint layer is set at the lining joint, and three types of contact conditions are forced to be satisfied through a parallel Lagrange multiplier network: Discontinuity condition (normal contact condition): The normal contact state of the joint is characterized by complementary constraints: the normal gap and normal contact force of the joint satisfy a non-negative mutually exclusive relationship. When the joint is closed, the normal gap is non-positive and the normal contact force is non-negative; when the joint is open, the normal gap is positive and the normal contact force is zero; in the critical closed state, the product of the normal contact force and the normal gap is always zero. This complementary condition ensures that the joint is either in a closed force transmission state or an open separation state, and there are no non-physical situations where the joint is closed but has no force or is open but has force.

[0028] The normal contact force is output through a Lagrange multiplier network and updated using an augmented Lagrange iterative scheme. The product of the current iteration's Lagrange multiplier value, the penalty parameter, and the current normal gap is summed. If the sum is positive, it is taken as the multiplier value for the next iteration; if the sum is negative, it is taken as zero, thus ensuring the non-negativity of the multipliers. The joint normal gap is obtained by calculating the projection of the displacement vector difference on both sides of the joint onto the local normal unit vector of the joint, and subtracting the initial joint opening value.

[0029] Formula for normal gap of joint: g = (u2 - u1) • n - g0; In the formula: g is the normal gap of the joint; u1 and u2 are the displacement vectors of the nodes on both sides of the joint; n is the normal unit vector of the joint; g0 is the initial opening of the joint.

[0030] Augmented Lagrange multiplier update formula: λ k+1 =max(λ) k +μ•g, 0); In the formula: λ k+1 For the updated normal Lagrange multiplier; λ k is the current normal Lagrange multiplier; μ is the penalty parameter; g is the joint normal gap.

[0031] Stress equilibrium condition (tangential contact condition): The tangential stress of the joint satisfies the classical friction law: the modulus of the tangential stress vector does not exceed the product of the normal contact force and the coefficient of friction. When the modulus of the tangential stress is less than this product, there is no relative slippage on both sides of the joint, and it is in an adhesive state; when the modulus of the tangential stress is equal to this product, relative slippage occurs at the joint, and the direction of the tangential stress is consistent with the direction of slippage.

[0032] Continuous seepage condition: Establishing a nonlinear coupling relationship between the permeability coefficient and the joint damage state: The joint damage variable is defined within a closed interval of zero to one, where zero represents the intact state of the material and one represents the completely damaged state. During the damage evolution process, the equivalent permeability coefficient is composed of two superimposed parts: the first part is the baseline permeability coefficient under the intact state, and the second part is the permeability enhancement term caused by damage. This enhancement term is proportional to the difference between the permeability coefficients under the intact and completely damaged states, and is also proportional to the power function of the damage variable. The preferred power exponent is in the range of 2-4. This range has been calibrated through a large amount of experimental data and can accurately reflect the nonlinear sudden increase in permeability coefficient during the formation of seepage channels caused by damage.

[0033] Permeability coefficient coupling formula: k = k0 + (k1 - k0) • d n ; In the formula: k is the equivalent permeability coefficient of the joint; k0 is the permeability coefficient in the intact state; k1 is the permeability coefficient in the fully damaged state; d is the joint damage variable; n is the damage-permeability coupling index.

[0034] The evolution of joint damage variables follows the stress-damage coupling law: the damage evolution rate is proportional to the power function of the equivalent stress exceeding the damage threshold, and also proportional to the power function of the remaining bearing capacity. The equivalent stress is either von Mises or Drucker-Prager equivalent stress, the damage threshold is determined based on concrete material strength tests, and the power exponent is calibrated based on damage evolution test curves.

[0035] The aforementioned joint damage evolution is embedded into the loss function along with the coupled process of seepage-stress-temperature-damage four fields. The loss function is constructed using a multi-objective weighted summation approach and includes three functional modules: The first module is the data fitting term, which is used to measure the deviation between the neural network prediction output and the field monitoring data or numerical reference solution, using mean square error or mean absolute error as the measure. The second module is the physical residual term, which is used to measure the degree to which the neural network output satisfies the control differential equation, including the residuals of the stress balance equation, the residuals of the seepage continuity equation, the residuals of the energy conservation equation, and the residuals of the damage evolution equation. The third module is the boundary condition term, which is used to measure the degree to which the neural network output satisfies the constraints of displacement boundary, stress boundary, and seepage boundary.

[0036] The three functional modules are weighted according to their importance: the physical residual term is multiplied by a first weighting factor, the boundary condition term by a second weighting factor, and the data fitting term by a unit weight. To ensure strict compliance with physical constraints, the second weighting factor is set to 10 to 100 times the first weighting factor. This weighting range was determined through numerical experiments, ensuring that physical conservation laws and boundary constraints are satisfied first while maintaining data fitting accuracy.

[0037] Loss function formula: Loss = Loss data +λ1•Loss phys +λ2•Loss bound ; In the formula: Loss is the total loss function; Loss data For data fitting terms; Loss phys For physical residuals; Loss bound λ1 represents the boundary condition term; λ2 represents the first weight; and λ3 represents the second weight.

[0038] S2: Establish a reduced-order model (POD-GPR) S201: Eigenorthogonal decomposition extracts dominant spatial modes Collect high-fidelity numerical solutions of four-field coupling under different operating conditions (called snapshots) and construct a snapshot matrix. Perform singular value decomposition on the snapshot matrix to obtain the singular values ​​corresponding to each mode. Calculate the ratio of the sum of squares of the singular values ​​of the first few modes to the sum of squares of the singular values ​​of all modes. This ratio represents the proportion of the contribution of the first few modes to the total energy of the original physical field.

[0039] The minimum number of modes that results in a cumulative energy percentage exceeding 99% is selected as the retained number of modes, and this number is controlled within the integer range of 10 to 30. This energy truncation criterion ensures that the reduced-order model retains the dominant dynamic characteristics of the original physical field while significantly reducing the dimensionality, thus reducing a full-order system with hundreds of thousands of degrees of freedom to a low-order system of 10 to 30 dimensions.

[0040] S202: Gaussian process regression establishes parameter mapping relationships Input parameters (including but not limited to surrounding rock grade, in-situ stress level, lining thickness, and material parameters) are mapped to modal coefficients to construct a Gaussian process regression surrogate model. The Gaussian process regression employs a Matérn-type kernel function or a radial basis function kernel function, optimizing the kernel function hyperparameters by maximizing the marginal likelihood function to establish a probabilistic mapping relationship from input parameters to modal coefficients.

[0041] For new input parameters, Gaussian process regression prediction not only provides the expected value of the modal coefficients but also the prediction variance, quantifying the prediction uncertainty. By linearly superimposing the predicted modal coefficients with the POD basis functions, the complete physical field distribution can be reconstructed.

[0042] S3: Real-time Prediction The trained hard-constraint physical information neural network is deployed on edge computing nodes at the tunnel site. The edge nodes receive real-time monitoring data from a distributed sensor network, including but not limited to physical quantities such as displacement, stress, seepage pressure, and temperature. Based on the hard-constraint physical information neural network, the state parameters of the surrounding rock and lining structure are inverted, including but not limited to surrounding rock mechanical parameters, initial in-situ stress, and damage distribution.

[0043] The parameters obtained from the inversion are input into the POD-GPR reduced-order model to quickly predict the evolution trend of the surrounding rock-lining coupled field in future periods. Since the computational complexity of the reduced-order model is only proportional to the cube of the number of modes, compared with the computational complexity of the full-order finite element method (which is proportional to the cube of the number of degrees of freedom), the computational efficiency is improved by 2 to 3 orders of magnitude, achieving millisecond-level response and meeting the requirements for real-time early warning.

[0044] S4: Federated Learning Collaborative Optimization S401: Local Training and Sensitivity Analysis Each tunnel section trains a hard-constraint physical information neural network locally to calculate the physical parameter sensitivity matrix. The elements of the sensitivity matrix are defined as the partial derivatives of the observed data with respect to the physical parameters, characterizing the degree of influence of each physical parameter on the system response. The sensitivity matrix is ​​constructed from the partial derivatives of the monitored response with respect to the physical parameters, calculated using automatic differentiation backpropagation; the matrix elements characterize the strength of the parameter's influence on the system output; the physical behavior similarity is taken as the reciprocal of the Euclidean distance of the sensitivity matrix, used for weighted aggregation in federated learning. Local convergence is achieved when the loss function changes by less than 10. -6 Alternatively, physical residuals less than 1% are used as the criterion; global convergence is defined as a change in global parameters of less than 10%. -4 The standard is that the accuracy does not improve for three consecutive rounds and the prediction error is less than 5%; the maximum number of iterations is set to 20-50 rounds to balance accuracy and efficiency.

[0045] S402: Weighted Aggregation The cloud server calculates a weighted aggregation weight based on geological condition similarity, physical behavior similarity, and local model accuracy. For the m-th tunnel segment, the aggregation weight is obtained by weighted summation of three parts: the first part is the geological condition similarity multiplied by a first coefficient, the second part is the sensitivity matrix similarity multiplied by a second coefficient, and the third part is the local model accuracy multiplied by a third coefficient. All three coefficients are positive and their sum is always equal to one.

[0046] Aggregate weight formula: w=α•S geo +β•S phy +γ•A CC ; In the formula: w is the aggregation weight; S geo Cosine similarity of geological conditions; S phy For physical behavior similarity; A CC α represents the accuracy of the local model; α, β, and γ are preset normalization coefficients.

[0047] Geological condition similarity is obtained by constructing geological feature vectors to represent attributes including but not limited to surrounding rock grade, lithological combination, and geological structural complexity, and by calculating the cosine of the angle between geological feature vectors of different tunnel sections; sensitivity matrix similarity is obtained by calculating the Euclidean distance between the sensitivity matrices of each tunnel and taking the reciprocal of the distance.

[0048] The global model parameters aggregated in the cloud are a weighted sum of the local model parameters of each tunnel, and the weights are the aggregate weights calculated above.

[0049] S403: Privacy Protection Before uploading model parameters, each tunnel section employs differential privacy processing, adding random noise conforming to a Gaussian distribution to the parameters. The noise variance is determined based on the privacy budget and model sensitivity. The original monitoring data is always stored locally, with only the noisy model parameters shared, satisfying the mathematical definition of differential privacy and effectively protecting data privacy.

[0050] The technical effects of the present invention are verified through specific embodiments below.

[0051] Example 1: Construction of a Hard-Constrained Physical Information Neural Network This embodiment provides a method for constructing a hard-constraint physical information neural network, the specific steps of which are as follows: Step 101: Network Architecture Design A deep neural network was constructed. The input layer contained 7 neurons, corresponding to the spatiotemporal coordinates (3 components), the elastic modulus of the surrounding rock, the elastic modulus of the lining, the permeability coefficient, and the temperature conductivity coefficient. The hidden layers adopted a 10-layer fully connected structure, with 80 neurons in each layer, and the Swish function was used as the activation function. The output layer contained 12 neurons, corresponding to 3 displacement components, 6 stress components, 1 pore water pressure, 1 temperature field, and 1 damage variable.

[0052] Step 102: Embedding the physical constraint layer A physical constraint layer is set at the lining joint. Assuming the joint is described by a spatial surface, the local coordinate system of the joint is defined: the normal unit vector is perpendicular to the joint surface and points to one side, and the two tangential unit vectors are located in the tangential plane of the joint and are orthogonal to each other.

[0053] Normal contact condition handling: A Lagrange multiplier network is constructed and trained in parallel with the main network to output the normal Lagrange multiplier (i.e., normal contact force). The joint normal gap is defined as the projection of the displacement vector difference on both sides of the joint onto the normal unit vector minus the initial joint opening. The multiplier is updated using an augmented Lagrange iterative scheme: the current multiplier value is summed with the product of the penalty parameter and the current normal gap, and the larger of this sum and zero is taken as the updated multiplier value.

[0054] The iterative process includes the following sub-steps: First, fix the current multiplier value and solve the minimization problem to obtain the current displacement field; then, calculate the new normal clearance based on the updated displacement field and update the multiplier value; finally, check the convergence condition. If the change in normal clearance between two adjacent iterations is less than the set tolerance, stop the iteration; otherwise, return to continue the iteration. The penalty parameter ranges from 1000 to 1000000 and is dynamically adjusted according to the problem stiffness.

[0055] Tangential friction condition handling: A return-mapping algorithm is used to handle frictional contact. First, the experimental tangential stress is calculated by subtracting the product of the penalty parameter and the tangential relative displacement from the current tangential stress. Then, it is determined whether the modulus of the experimental tangential stress is less than the product of the normal contact force and the coefficient of friction: if it is less, the bonded state is maintained and the tangential relative displacement is zero; if it is greater than or equal to, slippage occurs, and the tangential stress is projected onto the friction cone surface, i.e., the direction remains unchanged, and the modulus is taken as the product of the normal contact force and the coefficient of friction.

[0056] Step 103: Construction of the four-field coupling loss function Construct a loss function that includes a data fitting term, a physical residual term, and a boundary condition term.

[0057] The data fitting term measures the deviation between the neural network's predicted output and the field monitoring data or high-fidelity numerical solution, including the mean square error between the displacement prediction value and the monitored displacement, the mean square error between the stress prediction value and the monitored stress, and the mean square error between the pore water pressure prediction value and the monitored pressure.

[0058] The physical residual term measures the degree to which the neural network output satisfies the governing differential equation. The stress balance residual is obtained by calculating the vector difference between the stress divergence and the volume force; the seepage continuity residual is obtained by calculating the difference between the Darcy velocity divergence and the source-sink term; the energy conservation residual is obtained by calculating the difference between the heat flux density divergence and the internal heat source; and the damage evolution residual is obtained by calculating the difference between the damage variable's rate of change over time and the theoretical evolution rate.

[0059] The boundary condition term measures the degree to which the neural network output satisfies the boundary constraints, including displacement boundary residuals, stress boundary residuals, seepage boundary residuals, and temperature boundary residuals.

[0060] The loss function is a weighted summation: the data fitting term is multiplied by a unit weight, the physical residual term is multiplied by a first weight coefficient (ranging from 0.1 to 1.0), and the boundary condition term is multiplied by a second weight coefficient (10 to 100 times the first weight coefficient). This weighting configuration ensures that physical conservation laws and boundary constraints are satisfied first while fitting the data.

[0061] Step 104: Network Training The Adam optimizer was used for training, with an initial learning rate of 0.001. The learning rate was decayed by 50% every 1000 training epochs. An adaptive weight adjustment strategy was adopted during training: the weight coefficients were fixed for the first 5000 epochs, and then dynamically adjusted according to the convergence of the physical residuals to ensure that all types of residuals converged synchronously to below the set tolerance.

[0062] Example 2: Construction of an Intrinsic Orthogonal Decomposition-Gaussian Process Regression Model for Order Reduction This embodiment provides a method for constructing an intrinsic orthogonal decomposition-Gaussian process regression reduced-order model: Step 201: High-fidelity snapshot generation Fifty typical working conditions were selected, covering different surrounding rock grades (grades 3 to 5), ground stress levels (10 MPa to 30 MPa), lining thicknesses (30 cm to 60 cm), and groundwater heads (0 m to 50 m). Full-order finite element analysis was performed on each working condition, and commercial finite element software was used to solve the coupled four-field problem of seepage, stress, temperature, and damage, obtaining spatiotemporal snapshot data of the physical field.

[0063] Step 202: Extraction of intrinsic orthogonal decomposition modes Taking the stress field as an example, a snapshot matrix is ​​constructed, with the number of rows equal to the number of finite element nodes (50,000 in this embodiment) and the number of columns equal to the number of snapshots (50). Singular value decomposition is performed on the snapshot matrix to obtain 50 singular values ​​arranged in descending order. The ratio of the sum of squares of the first few singular values ​​to the sum of squares of all singular values ​​is calculated; this ratio represents the cumulative energy percentage.

[0064] The first 20 modes are selected, whose cumulative energy accounts for 99.5%, and an intrinsic orthogonal decomposition basis function matrix is ​​constructed. Any stress field distribution can be approximately represented as a linear superposition of the first 20 basis functions, and the superposition coefficient is the modal coefficient, realizing the projection from high-dimensional space (50,000 dimensions) to low-dimensional space (20 dimensions).

[0065] Step 203: Establishing the Gaussian process regression map A training dataset was established using 50 sets of input parameters (surrounding rock grade, in-situ stress, lining thickness, and water head) and their corresponding 20-dimensional modal coefficients. A Gaussian process regression model was trained for each modal coefficient using the Matérn5 / 2 kernel function. The length scale parameter and signal variance parameter of the kernel function were optimized by maximizing the log-marginal likelihood function.

[0066] Step 204: Online Prediction For the input parameters of the new working condition, the Gaussian process regression model outputs the expected value and prediction variance of the modal coefficients. The expected values ​​of the 20 modal coefficients are linearly superimposed with the corresponding basis functions to reconstruct the stress field distribution; the prediction variance is superimposed with the squares of the basis functions to quantify the uncertainty of the reconstructed stress field. A single prediction takes approximately 0.05 seconds, which is about 144,000 times more efficient than the 2 hours required for a full-order finite element solution.

[0067] Example 3: Federated Learning Collaborative Optimization. This example provides a cross-tunnel group federated learning method: Step 301: Local Model Training Suppose there are three tunnel sections participating in federated learning: Tunnel A (granite strata), Tunnel B (sandstone strata), and Tunnel C (limestone strata). Each tunnel trains a hard-constrained physical information neural network using its own monitoring data locally. After training, the accuracy of the local model on the validation set is calculated, and the physical parameter sensitivity matrix is ​​calculated using automatic differentiation techniques.

[0068] Step 302: Similarity Calculation Geological condition similarity is calculated by constructing a 5-dimensional geological feature vector. The five dimensions represent the uniaxial compressive strength of the surrounding rock, the rock mass integrity coefficient, the joint surface friction angle, the groundwater seepage coefficient, and the in-situ stress lateral pressure coefficient, respectively. The cosine value of the angle between the geological feature vectors of different tunnels is calculated, and the larger the cosine value, the more similar the geological conditions.

[0069] Physical behavior similarity is obtained by calculating the Euclidean distance between sensitivity matrices. First, each sensitivity matrix is ​​normalized. Then, the sum of squared differences between corresponding elements of the matrices is calculated, and the square root is taken to obtain the Euclidean distance. Finally, the reciprocal of the distance is taken as the similarity measure.

[0070] Step 303: Weighted Aggregation Calculate the aggregate weight for each tunnel. Taking tunnel A as an example, its weight consists of three parts: geological condition similarity multiplied by 0.4, physical behavior similarity multiplied by 0.3, and local model accuracy multiplied by 0.3. The sum of the three coefficients is always equal to 1, ensuring that the weight is normalized and conforms to geological and mechanical similarity.

[0071] The global model parameters aggregated in the cloud are a weighted sum of the local model parameters of each tunnel, with the weights being the aggregated weights calculated above. The aggregated global model is then distributed to each tunnel for local fine-tuning, starting the next round of federated learning iterations.

[0072] Step 304: Differential Privacy Protection Random noise is added to each tunnel before uploading model parameters. The noise follows a zero-mean Gaussian distribution, and its standard deviation is determined based on the privacy budget (set to 1.0) and model sensitivity. Model sensitivity is controlled by gradient pruning, with a pruning threshold set to 1.0 to ensure that the impact of a single sample on the model parameters does not exceed this threshold. The model parameters after adding noise satisfy the mathematical definition of differential privacy, making it impossible for attackers to infer the original monitoring data from the aggregated model.

[0073] Example 4: System Integration and Engineering Applications This embodiment provides an edge computing deployment solution: Edge servers are deployed at the tunnel site monitoring station, equipped with edge computing chips, with a computing power of no less than 32 trillion operations per second. The sensor network includes: displacement monitoring using a total station in conjunction with fiber optic grating sensors to monitor lining convergence deformation; stress monitoring using embedded concrete strain gauges to monitor the stress state of the lining; seepage monitoring using piezometers in conjunction with flow meters to monitor joint leakage; and temperature monitoring using a distributed fiber optic temperature measurement system to monitor the surrounding rock temperature field.

[0074] Edge nodes receive monitoring data in real time and invert the current state parameters of the surrounding rock-lining system through a hard-constrained physical information neural network. These parameters include, but are not limited to, the equivalent elastic modulus of the surrounding rock, the initial geostress field distribution, and the joint damage variable distribution. The inverted parameters are then input into an intrinsic orthogonal decomposition-Gaussian process regression model to predict the four-field coupled evolution trend over the next 24 hours.

[0075] When the prediction results show that the damage variable exceeds 0.8 and the seepage flow exceeds 10 L / min, a three-level early warning mechanism is triggered: Level 1 warning notifies on-site inspection personnel to strengthen monitoring; Level 2 warning initiates emergency drainage measures; Level 3 warning recommends closing traffic and structural reinforcement. Early warning information is pushed to the operation and maintenance management center in real time via mobile communication network.

[0076] The following are the experimental verification data: Experiment 1: Verification of Seam Contact Accuracy A lining structure model with a single joint was established, and calculations were performed using a traditional soft-constrained physical information neural network, a contact algorithm from commercial finite element software, and the hard-constraint method of this invention. Results show that the soft-constraint method has a normal clearance error of 12.3% and a tangential stress error of 18.7%; the finite element algorithm has a normal clearance error of 2.1% and a calculation time of 45 minutes; while the hard-constraint method has a normal clearance error of 1.8% and a tangential stress error of 3.2% and a calculation time of 8 minutes. The hard-constraint method significantly improves computational efficiency while maintaining high accuracy.

[0077] Experiment 2: Verification of the accuracy and efficiency of the reduced-order model A deep-buried tunnel (800m deep, 12km long) was selected, and the performance of different methods was compared: the full-order finite element method took 2.5 hours to calculate; the traditional intrinsic orthogonal decomposition reduced-order model took 15 minutes, with a stress field error of 8.5% and a seepage field error of 12.3%; the intrinsic orthogonal decomposition-Gaussian process regression model of this invention took 0.1 seconds, with a stress field error of 3.2% and a seepage field error of 4.8%. This invention achieves millisecond-level real-time prediction while ensuring accuracy.

[0078] Experiment 3: Validation of Federated Learning Effectiveness Comparing the model performance of local independent training and federated learning collaborative training: Tunnel A achieved a local training accuracy of 82.3% and a federated learning accuracy of 89.7%, an improvement of 7.4 percentage points; Tunnel B achieved a local training accuracy of 78.6% and a federated learning accuracy of 86.2%, an improvement of 7.6 percentage points; Tunnel C achieved a local training accuracy of 85.1% and a federated learning accuracy of 91.3%, an improvement of 6.2 percentage points. Federated learning significantly improves the model performance of all participating parties while protecting data privacy.

[0079] Next, refer to the appendix. Figure 2 A coupled analysis system for tunnel surrounding rock lining proposed according to an embodiment of the present invention is described.

[0080] Figure 2 This is a block diagram of the tunnel surrounding rock lining coupling analysis system 500 according to an embodiment of the present invention.

[0081] like Figure 2 As shown, the tunnel surrounding rock lining coupling analysis system 500 includes: Neural network construction module 501 is used to build a neural network containing an input layer, a hidden layer and a physical constraint layer. At the lining joint, the Lagrange multiplier network forces the satisfaction of displacement discontinuity condition, stress balance condition and seepage continuity condition, and embeds the joint damage evolution and the four-field coupling process of seepage-stress-temperature-damage into the loss function. The reduced-order model building module 502 is used to extract the four-field coupled dominant spatial modes through intrinsic orthogonal decomposition, and to establish the mapping relationship between input parameters and mode coefficients by combining Gaussian process regression, thereby constructing an intrinsic orthogonal decomposition-Gaussian process reduced-order surrogate model. The real-time prediction module 503 is used to deploy a hard-constrained physical information neural network on edge computing nodes, invert the state of the surrounding rock and lining structure based on monitoring data, input the inversion parameters into the reduced-order model, and predict the evolution of the coupling field between the surrounding rock and the lining.

[0082] It should be noted that the foregoing explanation of the embodiment of the coupling analysis method for tunnel surrounding rock lining also applies to the coupling analysis system for tunnel surrounding rock lining in this embodiment, and will not be repeated here.

[0083] Figure 3 This is a schematic diagram of an electronic device provided in an embodiment of the present invention. The electronic device may include: The memory 601, the processor 602, and the computer program stored on the memory 601 and capable of running on the processor 602.

[0084] When the processor 602 executes the program, it implements the tunnel surrounding rock lining coupling analysis method provided in the above embodiments.

[0085] Furthermore, electronic devices also include: Communication interface 603 is used for communication between memory 601 and processor 602.

[0086] The memory 601 is used to store computer programs that can run on the processor 602.

[0087] The memory 601 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0088] If the memory 601, processor 602, and communication interface 603 are implemented independently, then the communication interface 603, memory 601, and processor 602 can be interconnected via a bus to complete communication between them. The bus can be, but is not limited to, an industry-standard architecture bus, an external device interconnect bus, or an extended industry-standard architecture bus. The bus can be categorized, but is not limited to, an address bus, a data bus, and a control bus. For ease of representation, Figure 3 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0089] Optionally, in a specific implementation, if the memory 601, processor 602, and communication interface 603 are integrated on a single chip, then the memory 601, processor 602, and communication interface 603 can communicate with each other through an internal interface.

[0090] Processor 602 may be a central processing unit, a specific integrated circuit, or one or more integrated circuits configured to implement embodiments of the present invention.

[0091] This invention also provides a computer program product, which, when executed by a processor, implements the above-described method for coupled analysis of tunnel surrounding rock lining.

[0092] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for coupled analysis of tunnel surrounding rock lining.

[0093] This technology overcomes the industry pain points of traditional methods, such as low computational efficiency, insufficient prediction accuracy, and difficulty in ensuring data privacy. It has outstanding application value and broad prospects in the whole life cycle management of tunnel engineering and related geotechnical engineering fields, specifically in four aspects: Intelligent safety management and control during tunnel operation: It can be deployed on the field edge computing node to achieve millisecond-level accurate prediction of the four-field coupled evolution of surrounding rock and lining. It can promptly identify cracks and leakage hazards in lining joints and trigger graded early warnings, supporting emergency response and refined on-demand operation and maintenance. It can significantly improve the operational safety level of tunnels in complex working conditions such as deep burial, high water pressure, and soft rock, and reduce operation and maintenance costs.

[0094] Tunnel design and construction phase optimization: Compared with traditional numerical software, the reduced-order model achieves an order-of-magnitude improvement in simulation efficiency, can quickly complete the simulation of the coupling effect of different design schemes, and optimize design indicators such as lining thickness and support parameters; during the construction period, the surrounding rock-lining coupling response is predicted by combining real-time monitoring data, which guides the adjustment of procedures and effectively avoids the construction risks of face instability and early lining damage.

[0095] Technology transfer across geotechnical engineering scenarios: The core hard-constrained physical information neural network and reduced-order model architecture can be adapted to projects including but not limited to underground pipe corridors, slope foundation pits, water conservancy tunnels, and mine roadways. After fine-tuning the model, multi-field coupling analysis and risk prediction can be achieved, and the technology has strong reusability.

[0096] Empowering the digitalization and industrialization of industries: The federated learning architecture supports cross-regional collaborative modeling of tunnels, enabling knowledge transfer while protecting data privacy, and is adapted to the unified management and control of large-scale tunnel projects such as urban rail networks; relying on core algorithms, domestic engineering simulation software can be developed to replace foreign commercial tools, and it can also be integrated with intelligent tunnel monitoring hardware to form an integrated product of "sensing + edge computing + cloud collaboration", promoting the intelligent upgrading of tunnel monitoring equipment and assisting in the construction of smart geotechnical engineering.

[0097] Overall, this technology combines high precision, high real-time performance, and high security, aligning with the trend of digital infrastructure development. It serves as a core supporting technology for the full lifecycle management of tunnel engineering and provides a general solution for intelligent monitoring and control of geotechnical engineering. It has significant market demand and remarkable industrialization potential.

[0098] I. Construction Phase: Dynamically manage construction risks and adapt to highway tunnel construction conditions. For construction scenarios such as highway mountain tunnels and cross-river tunnels, the technology is deployed at temporary edge monitoring nodes during construction. It connects with sensor data on site, including but not limited to displacement, stress, and seepage pressure, to invert the coupling state of the surrounding rock with the initial support and secondary lining in real time, and predict the risks of stress concentration, joint cracking, and surrounding rock instability under excavation disturbance.

[0099] It provides rapid guidance on adjusting excavation spacing and support timing, and is particularly suitable for construction management in complex geological sections of highway tunnels, such as shallow-buried, biased, and water-rich areas. This helps avoid delays and safety accidents caused by construction risks, ensuring the progress and quality of highway tunnel construction.

[0100] II. Operational Phase: Achieve routine intelligent monitoring and tiered early warning systems to match highway operational needs. By embedding lightweight algorithms into the edge computing equipment of highway tunnel field monitoring stations, and connecting with routine monitoring data such as tunnel lining convergence, seepage, and stress, the evolution of four coupled fields can be predicted in milliseconds, accurately identifying lining leakage, joint damage expansion, and surrounding rock deformation.

[0101] Considering the characteristics of high traffic volume and the need to ensure smooth passage in highway tunnels, a tiered early warning mechanism tailored to highway operation and maintenance is established: minor hazards only require notification to strengthen monitoring, moderate hazards trigger emergency drainage and local traffic control, and severe hazards trigger lane closures / tunnel reinforcement. This ensures driving safety while minimizing the impact on highway traffic. At the same time, through structural condition inversion, on-demand maintenance is achieved, replacing the traditional periodic inspection mode, reducing the manpower cost of highway tunnel operation and maintenance, and extending the service life of the structure.

[0102] III. Design Phase: Efficiently optimize highway tunnel design schemes to improve economy and rationality. For core aspects of highway tunnel design, such as lining thickness, support parameters, and drainage design, a reduced-order model is used to achieve millisecond-level simulation calculations, replacing the traditional time-consuming full-order finite element analysis.

[0103] By quickly comparing the coupling effects of different design schemes and optimizing design indicators based on the load characteristics of highway tunnels (such as vehicle dynamic loads and surrounding rock stress), the amount of materials used can be reduced and the construction difficulty can be lowered while ensuring structural safety, thereby improving the economy and adaptability of highway tunnel design.

[0104] IV. Road Network Level: Supporting the coordinated management and control of highway tunnel clusters to achieve regional road network safety linkage. Based on the federated learning architecture of the technology, collaborative modeling and monitoring of multiple tunnels within the same highway network are carried out, and model knowledge transfer is achieved without disclosing the original monitoring data of each tunnel.

[0105] This addresses the issue of low prediction accuracy due to insufficient monitoring data for newly constructed highway tunnels, enabling unified status assessment and risk warning for regional highway tunnel groups. When a tunnel experiences a sudden malfunction, the system can quickly link with the road network management system to issue traffic alerts, achieving coordinated protection of highway network safety and traffic efficiency.

[0106] V. Special Scenarios: Adapting to the specific needs of highway tunnels For highway tunnels in special areas such as high-altitude, cold regions, and coastal areas, the technology can be embedded with temperature field coupling analysis to accurately predict lining damage caused by frost heave, thaw settlement, and salinization corrosion. For urban highway tunnels, the technology can be combined with the distribution of surrounding buildings and pipelines to invert the coupling impact of tunnel operation on the surrounding soil and rock, avoid road surface settlement and pipeline damage caused by tunnel deformation, and ensure the safety of urban highway supporting facilities.

[0107] Overall, when this technology is implemented in highway projects, the core features are lightweight deployment, customized parameters to fit highway operating conditions, and linkage with road network management. It does not require major modifications to the existing monitoring system. It only needs to connect with the existing sensor data and fine-tune the model to adapt to the load, geology, and operational characteristics of the highway tunnel. It can then be implemented quickly and become the core technical support for the safety management of highway tunnels throughout their entire life cycle.

[0108] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0109] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0110] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

[0111] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0112] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0113] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0114] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0115] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A coupled analysis method for tunnel surrounding rock lining, characterized in that, Includes the following steps: A hard-constrained physical information neural network is constructed, which includes an input layer, a hidden layer, and a physical constraint layer. At the lining joint, the displacement discontinuity condition, stress equilibrium condition, and seepage continuity condition are forced to be satisfied through a Lagrange multiplier network. The joint damage evolution and the four-field coupling process of seepage-stress-temperature-damage are embedded in the loss function. A reduced-order model is established by extracting the four-field coupled dominant spatial modes through intrinsic orthogonal decomposition and establishing the mapping relationship between input parameters and mode coefficients by combining Gaussian process regression, thus constructing an intrinsic orthogonal decomposition-Gaussian process reduced-order surrogate model. Real-time prediction involves deploying the hard-constrained physical information neural network on edge computing nodes, inverting the state of the surrounding rock and lining structure based on monitoring data, and inputting the inverted parameters into the reduced-order model to predict the evolution of the surrounding rock-lining coupled field.

2. The coupled analysis method for tunnel surrounding rock lining according to claim 1, characterized in that, The displacement discontinuity conditions are: the joint normal gap is less than or equal to zero, the normal Lagrange multiplier is greater than or equal to zero, and the product of the normal Lagrange multiplier and the joint normal gap is zero. The augmented Lagrange method is used to iteratively update the normal Lagrange multiplier. The update rule is: add the current normal Lagrange multiplier to the product of the penalty parameter and the current normal gap, compare the sum with zero, and take the larger value as the updated normal Lagrange multiplier. The joint normal gap is obtained by subtracting the joint opening from the projection of the displacement vector difference on both sides of the joint onto the joint normal unit vector.

3. The coupled analysis method for tunnel surrounding rock lining according to claim 1, characterized in that, The continuous seepage condition satisfies the coupling change of the permeability coefficient with the joint damage variable: the permeability coefficient is equal to the intact permeability coefficient, plus the difference between the fully damaged permeability coefficient and the intact permeability coefficient, and then multiplied by a specified exponent power of the joint damage variable; the specified exponent is the damage-permeability coupling exponent, with a value range of 2-4.

4. The coupled analysis method for tunnel surrounding rock lining according to claim 1, characterized in that, The loss function is obtained by adding three parts: a data fitting term, a first weight multiplied by a physical residual term, and a second weight multiplied by a boundary condition term; wherein, the first weight is the physical constraint weight, the second weight is the boundary constraint weight, and the second weight is 10-100 times the first weight.

5. The coupled analysis method for tunnel surrounding rock lining according to claim 1, characterized in that, The intrinsic orthogonal decomposition selects the first ten to thirtieth modes with a cumulative energy percentage greater than 99%.

6. The coupled analysis method for tunnel surrounding rock lining according to claim 1, characterized in that, It also includes federated learning collaborative optimization steps, including: Each tunnel locally trains the hard-constraint physical information neural network and calculates the physical parameter sensitivity matrix; The cloud platform calculates weighted aggregation weights based on geological condition similarity, physical behavior similarity, and local model accuracy, and then aggregates the models. Differential privacy processing is used before parameters are uploaded, and the original data is saved locally.

7. The coupled analysis method for tunnel surrounding rock lining according to claim 6, characterized in that, The aggregation weight is obtained by weighted summation of three parts: the first coefficient is multiplied by the cosine similarity of geological conditions, the second coefficient is multiplied by the reciprocal of the Euclidean distance of the physical parameter sensitivity matrix, and the third coefficient is multiplied by the accuracy of the local model; wherein, the first, second and third coefficients are preset normalization coefficients, all of which are positive numbers and the sum of the three is 1.

8. A coupled analysis system for tunnel surrounding rock lining, using the method described in any one of claims 1-7, characterized in that, include: The neural network construction module is used to establish a hard-constrained physical information neural network containing an input layer, a hidden layer, and a physical constraint layer. The physical constraint layer is set at the lining joint, and the displacement discontinuity condition, stress balance condition, and seepage continuity condition are forcibly satisfied through a parallel Lagrange multiplier network. The joint damage evolution and the four-field coupling process of seepage-stress-temperature-damage are embedded in the loss function. The reduced-order model building module is used to extract the four-field coupled dominant spatial modes through intrinsic orthogonal decomposition, and to establish the mapping relationship between input parameters and mode coefficients by combining Gaussian process regression, thereby constructing an intrinsic orthogonal decomposition-Gaussian process reduced-order surrogate model. The real-time prediction module is used to deploy a hard-constrained physical information neural network on edge computing nodes, invert the state of the surrounding rock and lining structure based on monitoring data, input the inversion parameters into a reduced-order model, and predict the evolution of the surrounding rock-lining coupled field.

9. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the method as claimed in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, It contains a computer program that enables the computer to perform the method as described in any one of claims 1-7.

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