Rock mass high-temperature deformation simulation method and system based on deep learning near-field dynamics

Abstract

The invention provides a rock mass high-temperature deformation simulation method and system based on deep learning near-field dynamics, and relates to the field of rock mass thermal-mechanical coupling analysis and research, and the method comprises the steps: obtaining the parameter information of a to-be-simulated target rock mass, including the geometric shape of the rock mass and the physical attribute of the rock mass; dispersing the target rock mass into a plurality of material points according to the parameter information, and constructing a thermal-mechanical coupling model of the target rock mass; based on the initialized thermal-mechanical coupling model, time step iterative simulation of a solid mechanical field is conducted, and finally the crack propagation process and temperature distribution of the target rock mass are obtained; according to the method, a solid field near-field dynamics theory based on strain energy density is introduced, a fluid field near-field dynamics equation is combined, temperature distribution in a rock medium is predicted through a physical information neural network, a deep learning near-field dynamics framework of rock mass high-temperature deformation damage is formed, and therefore rock mass high-temperature deformation is efficiently and accurately simulated.

Description

Technical Field

[0001] The present invention relates to the research field of rock mass thermal-mechanical coupling analysis, and specifically to a rock mass high-temperature deformation simulation method and system based on deep learning peridynamics. Background Art

[0002] In fields such as geothermal development and nuclear energy, the deformation and failure characteristics of rock masses under high-temperature environments directly impact the safety and stability of structures. Especially under variable temperature loads, rock mass mechanical properties undergo significant changes, such as thermal expansion, the generation of thermal stresses, and a reduction in strength, leading to crack expansion and failure. Effectively simulating the deformation and failure behavior of rock masses under high-temperature conditions has become a research priority in these fields.

[0003] Peridynamics (PD) is a relatively novel computational method that simulates the behavior of solid materials by defining nonlocal forces, thus avoiding the assumption of material continuity required in traditional methods. Unlike traditional methods, peridynamics can directly address discontinuities such as cracks and fractures and exhibits good adaptability. The peridynamic heat conduction equation, based on the principle of energy conservation, can effectively describe the thermal diffusion process in rock media.

[0004] However, it also has the disadvantage of low computational efficiency. Especially in large-scale calculations, the number of algorithm iterations and the amount of calculation increase exponentially. In particular, in the process of thermal-mechanical coupling solution, each solid field calculation time step is accompanied by a large number of temperature field iteration steps. Summary of the Invention

[0005] In order to solve the above problems, the present invention proposes a method and system for simulating high-temperature deformation of rock masses based on deep learning peridynamics. By introducing the solid field peridynamics theory based on strain energy density and combining it with the fluid field peridynamics equation, the temperature distribution in the rock medium is predicted through a physical information neural network, forming a deep learning peridynamics framework for high-temperature deformation and failure of rock masses, thereby efficiently and accurately simulating high-temperature deformation of rock masses.

[0006] According to some embodiments, the present invention adopts the following technical solutions: The rock mass high-temperature deformation simulation method based on deep learning peridynamics includes: Obtain parameter information of the target rock mass to be simulated, including the geometric shape and physical properties of the rock mass; According to the parameter information, the target rock mass is discretized into several material points and a thermal-mechanical coupling model of the target rock mass is constructed; Based on the initialized thermal-mechanical coupling model, a time-step iterative simulation of the solid mechanics field is performed to ultimately obtain the crack propagation process and temperature distribution of the target rock mass. Among them, in each iterative time step, first, based on the physical field information of the current time step, the neural network model is used to predict the temperature of each material point to obtain the temperature distribution of the current time step; then, according to the thermal-mechanical coupling effect of the rock, the physical field information is updated; secondly, based on the updated physical field information, it is judged whether the bond is broken, and the micromodulus and non-local force density are updated based on the judgment result; finally, based on the non-local force density, the physical field information is updated through the peridynamic control equation until the termination condition is triggered.

[0007] According to some embodiments, the present invention adopts the following technical solutions: The rock mass high-temperature deformation simulation system based on deep learning peridynamics includes: The information acquisition module is configured to: acquire parameter information of the target rock mass to be simulated, including the geometric shape and physical properties of the rock mass; The model building module is configured to: discretize the target rock mass into a number of material points according to parameter information, and build a thermal-mechanical coupling model of the target rock mass; The iterative simulation module is configured to: perform time-step iterative simulation of the solid mechanics field based on the initialized thermal-mechanical coupling model, and ultimately obtain the crack propagation process and temperature distribution of the target rock mass; Among them, in each iterative time step, first, based on the physical field information of the current time step, the neural network model is used to predict the temperature of each material point to obtain the temperature distribution of the current time step; then, according to the thermal-mechanical coupling effect of the rock, the physical field information is updated; secondly, based on the updated physical field information, it is judged whether the bond is broken, and the micromodulus and non-local force density are updated based on the judgment result; finally, based on the non-local force density, the physical field information is updated through the peridynamic control equation until the termination condition is triggered.

[0008] According to some embodiments, the present invention adopts the following technical solutions: A computer program product includes a computer program, which, when executed by a processor, implements the rock mass high-temperature deformation simulation method based on deep learning peridynamics.

[0009] According to some embodiments, the present invention adopts the following technical solutions: A non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the method for simulating high-temperature deformation of rock mass based on deep learning peridynamics is implemented.

[0010] According to some embodiments, the present invention adopts the following technical solutions: An electronic device comprises: a processor, a memory and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device implements the rock mass high-temperature deformation simulation method based on deep learning peridynamics.

[0011] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention establishes a stress analysis solution model by introducing a nonlocal differential operator, incorporates the proposed strain energy density change formula into the peridynamic micromodulus solution, and establishes a correlation between the mechanical parameters of the medium at the crack and the residual strain energy, which can more accurately consider the influence of crack propagation on the mechanical properties of the material.

[0012] (2) This invention effectively avoids the complexity of traditional peridynamic heat conduction iterative calculations and enables rapid temperature prediction in thermomechanical coupling simulations. Physical information neural networks embed physical laws into the training process, enabling efficient temperature distribution within each solid time step, significantly reducing computational time and resource consumption and improving simulation efficiency.

[0013] (3) This paper uses a physical information neural network to train peridynamic heat conduction results, which can capture the complex nonlinear relationship of thermal-mechanical coupling in fractured rock masses. Compared with traditional methods, the neural network model has stronger adaptive capabilities and can handle complex scenarios with different rock mass types and fracture distributions, thereby improving the accuracy of the simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0015] Figure 1 This is a flow chart of the method for simulating high-temperature deformation of rock masses based on deep learning peridynamics in Example 1. Figure 2 Schematic diagram of the peridynamic material point in Example 1.

[0016] Figure 3 This is the flow chart of the physical information neural network training of rock heat conduction in Example 1. DETAILED DESCRIPTION

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0019] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "comprising" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0020] Physical Information Neural Networks (PINNs) offer new insights into solving complex physical problems. By integrating physical laws with neural networks, PINNs can leverage vast amounts of historical data to train the network, capturing the complex relationships between input and output and providing efficient solutions. This paper, incorporating PINN technology within the existing peridynamics framework, proposes a method and system for simulating high-temperature rock deformation based on deep learning peridynamics. This approach establishes a novel deep learning peridynamics computational framework for high-temperature thermal-mechanical coupling of rock masses, overcoming the shortcomings of existing technologies and improving the accuracy and computational efficiency of peridynamic thermal-mechanical coupling simulations. This method is widely applicable to geotechnical engineering, geothermal development, nuclear energy engineering, fire protection, and other fields.

[0021] Example 1 In one embodiment of the present invention, a method for simulating high-temperature deformation of rock mass based on deep learning peridynamics is provided. Figure 1 Shown, including: Step 1: Obtain parameter information of the target rock mass to be simulated, including the geometric shape and physical properties of the rock mass; Step 2: Based on the parameter information, the target rock mass is discretized into several material points and a thermal-mechanical coupling model of the target rock mass is constructed; Step 3: Based on the initialized thermal-mechanical coupling model, perform time-step iterative simulation of the solid mechanics field to ultimately obtain the crack propagation process and temperature distribution of the target rock mass; Among them, in each iterative time step, first, based on the physical field information of the current time step, the neural network model is used to predict the temperature of each material point to obtain the temperature distribution of the current time step; then, according to the thermal-mechanical coupling effect of the rock, the physical field information is updated; secondly, based on the updated physical field information, it is judged whether the bond is broken, and the micromodulus and non-local force density are updated based on the judgment result; finally, based on the non-local force density, the physical field information is updated through the peridynamic control equation until the termination condition is triggered.

[0022] As an embodiment, the present invention's method for simulating high-temperature rock deformation based on deep learning peridynamics introduces solid field peridynamics theory based on strain energy density, combines it with fluid field peridynamic equations, and predicts the temperature distribution in the rock medium through a physical information neural network. This forms a deep learning peridynamics framework for high-temperature rock deformation and failure, thereby efficiently and accurately simulating high-temperature rock deformation. The specific implementation process is as follows: S1 introduces the solid field peridynamics theory based on strain energy density; By introducing the solid field peridynamics theory based on strain energy density, the solid field peridynamics control equations and nonlocal force density are constructed.

[0023] Specifically, the stress calculation process in solid field peridynamics theory is expressed as follows: (1) Among them, the coordinates of the target material point are expressed as , and is the relative position vector The weight, is an infinitesimal remainder, function is a known quantity, - is the change, is the partial differential symbol. For two-dimensional analysis, the derivative can be calculated using formula (1): (2) in, and Function for and The derivative of for Other interacting material points in the neighborhood A collection of material points Neighborhood, for 、 The relative position vector of is a two-dimensional space metric, etc. are non-local orthogonal functions, and is the corresponding order.

[0024] Furthermore, non-local orthogonal functions The following orthogonality is satisfied: (3) in, n 1. n 2.p 1. p 2 is the expansion order of the orthogonal function, ξ 1. ξ 2 is the component of ξ in the two coordinate directions, and is the Dirac function.

[0025] Furthermore, the peridynamic stress calculation in step S1 uses differential operators to represent the Navier equilibrium equation. In the two-dimensional case, the stress components can be constructed as: (4) (5) (6) Where, and are the elastic modulus and Poisson's ratio of the material, and Represents the displacement in two coordinate directions respectively.

[0026] At this point, by introducing the nonlocal differential operator, the stress analysis solution model represented by formulas (4)-(6) is established.

[0027] Further, Figure 2 is the principle diagram of peridynamic material points, such as Figure 2 As shown, Represents a material point The circular neighborhood of for Other interacting material points in the neighborhood, is the neighborhood radius, for The speed at time t, for 、 The relative position vector of is the relative displacement of the material point after the shape changes, based on Figure 2 The peridynamic material point principle in step S1 is used, and the solid field peridynamic control equation and nonlocal force density in step S1 are expressed as follows: (7) (8) in, for exist t The acceleration of time, is the solid density, for The physical strength of is the force density of classical peridynamics, Indicates the interaction point The volume, 、 They are 、 The position after deformation, is the relative displacement of the material point after the shape changes, is the micro potential energy at a point, is the micromodulus of the model, is the elongation of the key.

[0028] Elongation and The strain energy density at Respectively expressed as: (9) (10) in, Interaction point The volume, W is the strain energy density at a point.

[0029] Furthermore, S1 introduced the strain energy density theory to establish the effective elastic modulus of rock at the crack tip in different dissipation stages. and residual strain energy The nonlinear correspondence of elastic modulus is and initial elastic modulus same: (11) Crack initiation and expansion stages: (12) Post-peak softening stage: (13) Residual stage: (14) in, is the maximum value of residual strain energy, is the final value of the residual strain energy, a and b are constant positive numbers determined by experiments, usually b>a, is the residual effective elastic modulus.

[0030] The proposed strain energy density variation formula (i.e., Formulas 11-14) was incorporated into the peridynamic micromodulus solution, and the relationship between the mechanical parameters of the medium at the crack and the residual strain energy was established.

[0031] Specifically, for two-dimensional analysis, the micromodulus can be determined based on the effective elastic modulus at different stages. : (15) in, is the effective elastic modulus, is the neighborhood radius, is the thickness, is Poisson's ratio, micromodulus As the loading process changes, the non-local force density is updated in real time, and then Equation (8) (i.e., non-local force density) can be updated as: (16) in, Material point 、 The relative position vector between is the relative displacement of the material point after the shape changes.

[0032] Nonlocal force density Effective elastic modulus and elongation s The effective elastic modulus is determined by the residual strain energy at the calculation point. Sure.

[0033] Furthermore, material points and The function of the bond breaking state is , when the function Indicates that the connecting bond is not broken and there is non-local force density. When the function When , the bond breaks and the nonlocal force density disappears.

[0034] The damage degree at x is defined as: (17) when When , it means that all bonds at x are broken and the point is completely destroyed.

[0035] S2 constructs the near-field dynamics theory of temperature field diffusion in fractured rock mass; Furthermore, in the S2 temperature field peridynamics theory, the heat conduction process occurs in a non-local influence domain of a certain size, and the material point and The key between is considered as a heat conduction channel, then t time Heat flux for: (18) in, is the relative position vector, Rock material point and The macroscopic heat transfer coefficient between is the temperature difference between the two material points at time 𝑡, is the unit direction vector of the bond in the reference coordinate system.

[0036] According to the conservation of thermal energy, the governing equation for peridynamic heat conduction is: (19) in, ρ is the material density, c v is the specific heat capacity of the material, Material point temperature, The heat generated per unit volume outside, The nonlocal thermal conductivity of the material can be determined from the equivalence between the peridynamic heat flux and the heat flux in traditional continuum theory. For a 2D analysis: (20) in, is the macroscopic heat transfer coefficient Abbreviation of is the neighborhood radius, For thickness.

[0037] Furthermore, during the heat conduction process of rocks, if the rocks are cracked, the heat conduction mode in the cracks is complex. In addition to the heat conduction of the solid part of the rock, heat can also be conducted through the medium in the cracks. The difference in thermal conductivity of different media leads to significant changes in the heat conduction process. The effective thermal conductivity coefficient is used at the damaged part. K eff Taking into account the impact: (twenty one) in, dmg is the damage degree of the material point, is the macroscopic heat transfer coefficient, K M is the thermal conductivity of the medium in the crack, a R and b M is a constant that can be determined through experiments. If the crack is filled with water or other fluids, the conductivity K M The conductivity will increase, and the heat flow will extend along the cracks instead of simply being transmitted along the solid part of the rock; if the cracks are dry or filled with gas, the conductivity will decrease.

[0038] In heat conduction calculations, and The average value of the thermal conductivity between: (twenty two) in, and They are and Thermal conductivity coefficient, specifically the macro thermal conductivity coefficient of the rock when it is not broken K R Or the effective thermal conductivity after rupture K eff .

[0039] S3 establishes a physical information neural network framework for predicting temperature distribution in rock media; Furthermore, S3 establishes a physical information neural network framework to predict the temperature distribution in rock media, and its architecture includes: input layer, hidden layer and output layer.

[0040] The features of the input layer need to fully describe the information of the material points and ensure that the input With output Match between features, select the material point spatial coordinate position x, and the corresponding thermal conductivity coefficient K As input: (twenty three) in sta () represents the normalization of input features, thermal conductivity K Including the macroscopic thermal conductivity of the rock when it is not broken K R and the effective thermal conductivity after rupture K eff , in addition, the number of neurons in the input layer is equal to the number of features.

[0041] Furthermore, in order to capture the nonlinear relationship between input and output, multiple hidden layers are set, and appropriate methods are selected for hyperparameter adjustment to determine the appropriate network depth, including but not limited to grid search, random search, Bayesian optimization, etc.

[0042] Furthermore, all hidden layers use nonlinear activation functions, including but not limited to RELU, SELU, Sigmoid, Tanh, etc., which are all capable of performing model training tasks. Among them, the RELU activation function is relatively simple to calculate and can accelerate training: (twenty four) When input d When it is greater than 0, the output is d When input dWhen it is less than or equal to 0, the output is 0. In addition, ReLU does not have the gradient disappearance problem compared to Sigmoid and is suitable for deep networks. The output layer is the temperature distribution T (x), without the need for nonlinear activation functions: (25) Furthermore, to ensure that the neural network can be trained effectively, the input thermal conductivity coefficient K is properly preprocessed and a normalization method (Z-Score Normalization) is selected to effectively accelerate training. This ensures that all input data has the same dimension, thus avoiding instability in training caused by excessive magnitude of certain features: (26) in, K ave is the mean of the data, σ K is the standard deviation.

[0043] In order to expand the training set, the input data coordinates are randomly translated to increase the diversity of the data, thereby improving the generalization ability of the model. x 1 and x Add d at each of the two locations x 1 and d x 2. The original coordinates are transformed into ( x 1+d x 1, x 2+ d x 2).

[0044] Furthermore, during the forward propagation of model training, the input data Calculate the predicted value through the network layer , the number of hidden layers of the neural network is L, then the calculation of each layer is expressed as: (27) in, l is the hidden layer, The output of each layer is the input of the next layer. is the activation function (ReLU for hidden layers and linear activation for output layers), and For the l The weight matrix and bias vector in the layer.

[0045] Furthermore, to ensure that the output of the neural network satisfies the physical constraints of the peridynamic equations, the residual between the temperature prediction value and the actual value is calculated. L heat As part of the loss term: (28) in, and Respectively i The actual temperature value and predicted temperature value of each material point, N is the total material points.

[0046] The boundary conditions can be fixed temperature boundary conditions (Dirichlet boundary conditions) or heat flux boundary conditions (Neumann boundary conditions).

[0047] For Dirichlet boundary conditions (given the temperature value at a certain point), the loss function is expressed as: (29) For Neumann boundary conditions (such as the heat flux density at a given point), the loss function is expressed as: (30) in, L bd is the boundary condition loss term, where and The boundary bd The actual temperature value and predicted temperature value of each material point, N bc is the total number of boundary material points, is the true heat flux on the boundary, is the temperature gradient in the direction normal to the boundary.

[0048] Furthermore, to ensure that the network can consider the heat flux transfer between material points when predicting temperature distribution, an additional loss term is introduced to calculate the predicted heat flux between each pair of adjacent material points. and the real heat flux For comparison, the formula is: (31) (32) in, L flux is the heat flux loss term, Rock material point and The thermal conductivity between the two, including the macro thermal conductivity K R and effective thermal conductivity K eff .

[0049] Combining all the above loss terms, we can get the total loss function of the physical information neural network Ltotal : (33) Furthermore, backpropagation calculates the gradient of the loss function with respect to each parameter and updates the parameters by gradient descent.

[0050] The gradients of the output layer and the hidden layer are: (34) (35) in, For the l A linear combination of layers, represents the gradient term, is the derivative of the activation function, and ⊙ represents element-wise multiplication.

[0051] The weight matrix and bias vector are: (36) In order to avoid constructing the complete derivative expression, AD automatic differentiation is used to solve the gradient calculation.

[0052] S4 forms a rock mass with a thermal-mechanical coupling deep learning peridynamic algorithm.

[0053] Furthermore, the S4 deep learning peridynamics algorithm for rock mass thermal-mechanical coupling incorporates the fractured rock mass temperature distribution prediction model trained in S3 into the peridynamics thermal-mechanical coupling calculations. The S3 prediction model is used to quickly determine the fractured rock mass temperature distribution during each solid mechanics time step, eliminating the numerous heat conduction iterations required by traditional dynamics methods in S2 and significantly improving computational efficiency.

[0054] Furthermore, after quickly obtaining the temperature distribution of the rock mass, based on the thermal-mechanical coupling effect of the rock, the force density after coupling the solid mechanical field can be expressed as: (37) in, α represents the thermal expansion coefficient of rock material. Combining equations (7) and (15), we can obtain the peridynamic thermomechanical coupling equation of the strain energy density softening criterion under two-dimensional analysis: (38) The bond break state function updated over time steps: (39) in, s 0 is the critical value of bond breaking, which is related to the critical energy release rate of rock. for and The average value of temperature, where 0 and 1 represent broken and intact bonds, respectively.

[0055] Furthermore, as the mechanical field is iteratively calculated, the fractured rock mass is gradually damaged, and the effective thermal conductivity changes accordingly according to Equation (21). The updated effective thermal conductivity is used to predict the temperature distribution in the next time step after the change occurs. The newly predicted temperature distribution is fed back to Equations (38) and (39), realizing the coupling process.

[0056] Example 2 In one embodiment of the present invention, a rock mass experimental verification process of a rock mass high-temperature deformation simulation method based on deep learning peridynamics is provided, wherein a two-dimensional three-point bending rock beam is used as a standard fracture specimen, including: 1. Specimen and discreteness.

[0057] This example uses a two-dimensional three-point bent rock beam as a standard fracture specimen, with uniform geometric dimensions: length L = 0.20 m, height h = 0.05 m, and thickness t = 0.01 m. A type I straight crack is prefabricated in the center of the beam bottom, with an initial crack length of 0.01 m to ensure that the crack tip is located in the pure bending region. The entire computational domain is discretized using a uniform square grid, with a material point spacing of 1 mm, for a total of 10,000 material points. The neighborhood radius δ of each point is 3.015 mm, meeting the convergence requirements of peridynamics while also taking into account computational efficiency.

[0058] 2. Material parameters.

[0059] Initial elastic modulus of rock , Poisson's ratio ν = 0.3, density In order to describe the mechanical residual behavior after cracking, the key parameter of residual strain energy is introduced: , reflects the upper limit of material energy dissipation during crack propagation and is the residual strain energy density when the crack is completely destroyed; This reflects the residual energy remaining at the crack tip after crack propagation is complete. The empirical constants were determined by inverting the curve of an indoor three-point bend test, yielding a = 2.0 and b = 3.5, satisfying the requirement that b > a.

[0060] 3. Real-time calculation of residual strain energy.

[0061] During the calculation process, the strain energy density of each material point W Directly calculated from the current micro potential energy state:

[0062] When the bond elongation s Exceeding the critical value of bond breaking s 0, energy begins to dissipate. Residual strain energy density Updated in incremental manner.

[0063] 4. Phased update.

[0064] Effective elastic modulus and residual strain energy There is a nonlinear correspondence, for the elastic modulus in the elastic stage and initial elastic modulus same:

[0065] Crack initiation and expansion stages:

[0066] Post-peak softening stage:

[0067] Residual stage:

[0068] 5. Dynamic assignment of micromodulus c.

[0069] In the framework of bond-based peridynamics, the micromodulus of a material point is linearly related to the current effective elastic modulus:

[0070] Therefore, when the crack tip enters the softening or residual stage, the effective elastic modulus decreases rapidly, resulting in a micro-modulus c Synchronous reduction, non-local force density It automatically decreases as the key elongates, and the macroscopic manifestation is a rapid drop in bearing capacity, which is consistent with the test curve.

[0071] 6. Result verification.

[0072] When the loading displacement reaches 0.2 mm, the residual strain energy density is measured at the material point 1 mm in front of the crack tip. The error is less than 5% when compared with the local effective stiffness back-calculated from digital image correlation (DIC) tests. The crack propagation path is smooth and has no mesh dependence, which fully verifies the effectiveness and practicality of the nonlinear stiffness degradation model driven by residual strain energy in the near-field dynamic simulation of fractured rock masses.

[0073] Example 3 In one embodiment of the present invention, a specific process of constructing and training a neural network model in a rock mass high-temperature deformation simulation method based on deep learning peridynamics is provided, taking a two-dimensional single-crack sandstone plate as an object, such as Figure 3 Shown, including: 1. Overview.

[0074] This example uses a two-dimensional single-crack sandstone slab with geometric dimensions of 0.4m × 0.2m to simulate a single-crack granite temperature unit in an underground rock mass. A straight crack, 0.1m long and with a 0-degree inclination, is preset within the slab, located at the slab's centerline. Different constant temperatures are applied to the left and right boundaries, while the upper and lower edges are set as adiabatic boundaries. The model achieves a high-precision mapping from "spatial coordinates + conductivity" to "node temperature" by training a four-hidden-layer, fully connected physical information neural network. This model then replaces the traditional iterative temperature solution in subsequent thermal-mechanical coupling calculations, significantly improving computational efficiency while ensuring accuracy.

[0075] 2. Data preparation.

[0076] In order to obtain sufficiently rich and physically credible training samples, we first use the traditional peridynamic heat conduction solution to generate a database. The specific steps are as follows: (1) The combination of constant temperature conditions at the left and right boundaries takes 10 levels; the thermal conductivity of the rock matrix takes 5 levels; and the thermal conductivity of the fracture filling medium takes 5 levels.

[0077] (2) For each combination steady-state calculation, a 1 mm uniform grid is used for discretization, with a total number of nodes of approximately 80,000. After the calculation is completed, the coordinates, current thermal conductivity, and steady-state temperature are extracted at each node.

[0078] (3) The simulation results were divided into training set, validation set and test set according to the ratio of 8:1:1 to ensure statistical consistency. The Z-Score normalization method was used to process the initial data.

[0079] (4) Randomly shift the coordinates and apply uniform noise to the permeability to generate an additional 20% samples to improve the robustness of the model.

[0080] 3. PINN network structure.

[0081] The network has a fully connected feedforward architecture: the input layer has 3 neurons; hidden layer 1 has 64 neurons with a tanh activation function; hidden layer 2 has 128 neurons with a tanh activation function; hidden layer 3 has 128 neurons with a tanh activation function; hidden layer 4 has 64 neurons with a tanh activation function; and the output layer has 1 neuron with linear activation. Weights are initialized using Xavier uniform initialization, and biases are initialized to 0. To prevent overfitting, dropout is applied after hidden layers 2 and 3, with a dropout probability of 0.05.

[0082] 3. Training configuration.

[0083] The total loss function consists of three weighted terms: data loss, boundary loss, and heat flux loss. The empirical weights are determined via grid search. Training is performed in two phases: the first phase uses the Adam optimizer with a learning rate of 1e-3, weight decay of 1e-4, and a batch size of 4096 for 5000 steps. The second phase switches to L-BFGS fine-tuning with a maximum iteration of 1000 steps. During the Adam phase, the learning rate is decayed by 0.8 every 1000 steps. Early stopping is performed on the validation set, and training is terminated after no improvement for 20 consecutive steps. Training is completed on a single RTX-3070 GPU.

[0084] 4. Verification after training.

[0085] Test set results: mean absolute error MAE = 0.31 ° C, root mean square error RMSE = 0.46 ° C, maximum relative error < 3%, located in the crack tip area; determination coefficient , indicating that the network has good generalization ability.

[0086] Example 4 In one embodiment of the present invention, a specific implementation example of a method for simulating high-temperature deformation of rock mass based on deep learning peridynamics is provided, including: 1. Solution domain construction. Initialize the computational domain, input the rock mass geometry, fracture location, and density, elastic modulus, Poisson's ratio, specific heat capacity, thermal expansion coefficient, and thermal conductivity of the rock matrix and fracture medium. Calculate and store the effective thermal conductivity based on the fracture damage state to form a thermal property field that can evolve with damage.

[0087] 2. Initialize the calculation parameters. Set the total number of material points, neighborhood radius, initial displacement, initial temperature, boundary condition type and value; generate the coordinates of all material points and establish an adjacency list; assign an initial micromodulus, initial fracture state, and initial nonlocal force to each bond; set the time step length, total calculation time, and data output frequency.

[0088] 3. Prediction model deployment: Load the trained fractured rock mass temperature distribution prediction model in a callable format; the input interface binds the current material point coordinates and effective thermal conductivity; the output interface directly returns the temperature value of each material point without additional format conversion.

[0089] 4. Thermal-mechanical coupled time marching. At the beginning of each solid mechanics time step, the prediction model is called to obtain the global temperature distribution. The resulting temperature field is passed to the solid mechanics solver. Thermal stresses are calculated based on the temperature increment, and the nonlocal force density is updated. The peridynamic equations of motion are executed to solve the acceleration, velocity, and displacement of the material point. Bond breakage is determined based on bond elongation. If broken, the damage variable and effective thermal conductivity are updated.

[0090] Example 5 In one embodiment of the present invention, a specific implementation example of a method for simulating high-temperature deformation of rock mass based on deep learning peridynamics is provided, including: A1 solves the region construction; A2 calculation parameter initialization; A3 prediction model training; A4 thermal-mechanical coupled simulation; A5 result analysis.

[0091] Furthermore, the main contents of the A1 solution area construction are: initializing the solution domain and defining the geometric shape of the fractured rock mass, including parameters such as the thickness, length, and fracture distribution of the rock mass; setting the physical properties of the rock mass, such as the elastic modulus, Poisson's ratio, density, specific heat capacity, and thermal conductivity coefficient, and determining the effective thermal conductivity coefficient from the fracture damage area to ensure that the solution model can truly reflect the thermal-mechanical coupling behavior of the rock mass.

[0092] Furthermore, the main contents of A2 calculation parameter initialization are: according to the structural characteristics of the fractured rock mass, setting calculation parameters, including the number of material points, neighborhood radius, boundary conditions and other information; configuring non-local differential operators, bond micromodulus, strain energy density, non-local calculated thermal conductivity and other parameters; discretizing the solution domain according to these calculation parameters, and generating material point coordinates to determine the adjacent material points within the domain of each material point; initializing the bonds and non-local forces of the material point in its near field, and initializing the displacement, temperature and other information of the material point.

[0093] Furthermore, the main contents of the A3 prediction model training are as follows: the numerical results of the near-field dynamics heat conduction simulation are used as the training set, and various boundary conditions and initial damage states are changed to increase the number of training sets, and at the same time, a test set is divided; the data such as the thermal conductivity coefficient is normalized, and the network structure is determined and the weights and biases are initialized; the training set data is input into the neural network, and the predicted value and loss function value are calculated through forward propagation; automatic differentiation is used to update the weights and biases of the neural network according to the loss function value, and back propagation is performed; the above process is repeated until the total loss function converges or the preset number of training rounds is reached; the final performance of the model is evaluated using the test set data, and if the model performance is poor, the network structure is adjusted.

[0094] Furthermore, the main contents of the A4 thermal-mechanical coupling simulation are: deploying the trained temperature prediction model to carry out thermal-mechanical coupling simulation of fractured rock mass; directly using the neural network model to quickly obtain the material point temperature in each iterative time step of the solid mechanics field; calculating the non-local force, acceleration, displacement, stress and other information of each material point. If the elongation is greater than the set critical failure elongation, the bond non-local force between the material points disappears, and the damage and effective thermal conductivity coefficient are updated; the updated information is then fed back to the prediction model, and the material point temperature of the next iterative time step is obtained to realize coupled calculation until the calculation termination condition is triggered.

[0095] Furthermore, the main contents of A5 result analysis are: outputting the thermal-mechanical coupling simulation results of fractured rock mass, visualizing and analyzing the crack propagation process and temperature distribution of the rock mass.

[0096] Example 6 In one embodiment of the present invention, a rock mass high-temperature deformation simulation system based on deep learning peridynamics is provided, comprising: The information acquisition module is configured to: acquire parameter information of the target rock mass to be simulated, including the geometric shape and physical properties of the rock mass; The model building module is configured to: discretize the target rock mass into a number of material points according to parameter information, and build a thermal-mechanical coupling model of the target rock mass; The iterative simulation module is configured to: perform time-step iterative simulation of the solid mechanics field based on the initialized thermal-mechanical coupling model, and ultimately obtain the crack propagation process and temperature distribution of the target rock mass; Among them, in each iterative time step, first, based on the physical field information of the current time step, the neural network model is used to predict the temperature of each material point to obtain the temperature distribution of the current time step; then, according to the thermal-mechanical coupling effect of the rock, the physical field information is updated; secondly, based on the updated physical field information, it is judged whether the bond is broken, and the micromodulus and non-local force density are updated based on the judgment result; finally, based on the non-local force density, the physical field information is updated through the peridynamic control equation until the termination condition is triggered.

[0097] Example 7 In one embodiment of the present invention, a computer program product is provided, comprising a computer program, which, when executed by a processor, implements the method for simulating high-temperature deformation of rock masses based on deep learning peridynamics.

[0098] Example 8 In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided, which is used to store computer instructions. When the computer instructions are executed by a processor, the method for simulating high-temperature deformation of rock mass based on deep learning peridynamics is implemented.

[0099] Example 9 In one embodiment of the present invention, an electronic device is provided, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the rock high-temperature deformation simulation method based on deep learning peridynamics.

[0100] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0101] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0102] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. A rock mass high-temperature deformation simulation method based on deep learning peridynamics, characterized by: include: Obtain parameter information of the target rock mass to be simulated, including the geometric shape and physical properties of the rock mass; According to the parameter information, the target rock mass is discretized into several material points and a thermal-mechanical coupling model of the target rock mass is constructed; Based on the initialized thermal-mechanical coupling model, a time-step iterative simulation of the solid mechanics field is performed to ultimately obtain the crack propagation process and temperature distribution of the target rock mass. Among them, in each iterative time step, first, based on the physical field information of the current time step, the neural network model is used to predict the temperature of each material point to obtain the temperature distribution of the current time step; then, according to the thermal-mechanical coupling effect of the rock, the physical field information is updated; secondly, based on the updated physical field information, it is judged whether the bond is broken, and the micromodulus and non-local force density are updated based on the judgment result; finally, based on the non-local force density, the physical field information is updated through the peridynamic control equation until the termination condition is triggered.

2. The method for simulating high-temperature deformation of rock mass based on deep learning peridynamics according to claim 1, characterized in that: The geometric shape includes the thickness, length, and crack distribution of the rock mass; the physical properties include the elastic modulus, Poisson's ratio, density, specific heat capacity, and thermal conductivity of the rock mass.

3. The method for simulating high-temperature deformation of rock mass based on deep learning peridynamics according to claim 1, characterized in that: The thermomechanical coupling model introduces the solid field peridynamics theory based on strain energy density and combines it with the fluid field peridynamics equation to construct the peridynamic thermomechanical coupling equation with the strain energy density softening criterion.

4. The method for simulating high-temperature deformation of rock mass based on deep learning peridynamics according to claim 1, characterized in that: The neural network model adopts a physical information neural network PINN, which takes the physical field information of the physical point as input and the temperature value of the material point as output; wherein the physical field information includes coordinates and effective thermal conductivity coefficient.

5. The method for simulating high-temperature deformation of rock mass based on deep learning peridynamics according to claim 1, characterized in that: The updating of physical field information according to the thermal-mechanical coupling effect of the rock is specifically as follows: Calculate thermal stress based on temperature increment and update nonlocal force density; execute fluid field peridynamic equations and solve physical field information of material points.

6. The method for simulating high-temperature deformation of rock mass based on deep learning peridynamics according to claim 1, characterized in that: The method of determining whether a bond is broken based on the updated physical field information and updating the micromodulus and non-local force density based on the determination result is as follows: Determine the fracture state based on the elongation between two material points; If fracture occurs, the damage degree is calculated, and the residual strain energy and micromodulus of the material point are calculated based on the damage degree; Update the nonlocal force density based on the effective elastic modulus from the elongation and micromodulus.

7. A rock mass high temperature deformation simulation system based on deep learning peridynamics, characterized by: include: The information acquisition module is configured to: acquire parameter information of the target rock mass to be simulated, including the geometric shape and physical properties of the rock mass; The model building module is configured to: discretize the target rock mass into a number of material points according to parameter information, and build a thermal-mechanical coupling model of the target rock mass; The iterative simulation module is configured to: perform time-step iterative simulation of the solid mechanics field based on the initialized thermal-mechanical coupling model, and ultimately obtain the crack propagation process and temperature distribution of the target rock mass; Among them, in each iterative time step, first, based on the physical field information of the current time step, the neural network model is used to predict the temperature of each material point to obtain the temperature distribution of the current time step; then, according to the thermal-mechanical coupling effect of the rock, the physical field information is updated; secondly, based on the updated physical field information, it is judged whether the bond is broken, and the micromodulus and non-local force density are updated based on the judgment result; finally, based on the non-local force density, the physical field information is updated through the peridynamic control equation until the termination condition is triggered.

8. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for simulating high-temperature deformation of rock mass based on deep learning peridynamics according to any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium, characterized in that The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the method for simulating high-temperature deformation of rock mass based on deep learning peridynamics as described in any one of claims 1 to 6 is implemented.

10. An electronic device, characterized in that: include: A processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the high-temperature deformation simulation method of rock mass based on deep learning peridynamics as described in any one of claims 1 to 6.

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