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

Abstract

The application provides a rock mass high-temperature deformation simulation method and system based on deep learning near-field dynamics, relates to the field of rock mass thermal-mechanical coupling analysis and research, and comprises the following steps: obtaining parameter information of a target rock mass to be simulated, including the geometric shape of the rock mass and the physical properties of the rock mass; according to the parameter information, the target rock mass is discretized into a plurality of material points, and a thermal-mechanical coupling model of the target rock mass is constructed; based on the initialized thermal-mechanical coupling model, time step iteration simulation of the solid mechanics field is performed, and finally the crack propagation process and temperature distribution of the target rock mass are obtained; by introducing the solid field near-field dynamics theory based on strain energy density, combining the fluid field near-field dynamics equation, predicting the temperature distribution in the rock medium through the physical information neural network, and forming the deep learning near-field dynamics framework of rock mass high-temperature deformation and failure, the rock mass high-temperature deformation can be simulated efficiently and accurately.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rock mass thermal coupling analysis, and particularly relates to a rock mass high-temperature deformation simulation method and system based on deep learning peridynamics. BACKGROUND

[0002] In the fields of geothermal development, nuclear energy, etc., the deformation and failure characteristics of rock mass under high-temperature environment directly affect the safety and stability of the structure. Especially under the variable temperature load, the mechanical properties of rock mass will change significantly, such as thermal expansion, generation of thermal stress, and reduction of strength, resulting in crack propagation, failure, etc. How to effectively simulate the deformation and failure behavior of rock mass under high-temperature conditions has become a research focus in the relevant field.

[0003] Peridynamics (PD) is a relatively novel calculation method, which simulates the behavior of solid materials by defining non-local forces, thereby avoiding the assumption of material continuity in traditional methods. Unlike traditional methods, peridynamics can directly handle discontinuous problems such as cracks and fractures, and has good adaptability. The peridynamics heat conduction equation based on the principle of energy conservation can well describe the thermal diffusion process of rock mass medium.

[0004] However, it also has the disadvantage of low calculation efficiency, especially in large-scale calculations, the number of iterations and the amount of calculation of the algorithm increase exponentially, especially in the process of solving thermal coupling, each solid field calculation time step is accompanied by a large number of temperature field iteration steps. SUMMARY

[0005] To solve the above problems, the present application proposes a rock mass high-temperature deformation simulation method and system based on deep learning peridynamics, which introduces a solid field peridynamics theory based on strain energy density, combines with a fluid field peridynamics equation, predicts the temperature distribution in rock medium through a physical information neural network, forms a deep learning peridynamics framework for rock mass high-temperature deformation and failure, and thus efficiently and accurately simulates the rock mass high-temperature deformation.

[0006] According to some embodiments, the present application adopts the following technical solutions:

[0007] The rock mass high-temperature deformation simulation method based on deep learning peridynamics comprises:

[0008] Obtaining parameter information of a target rock mass to be simulated, including the geometric shape of the rock mass and the physical properties of the rock mass;

[0009] Discretizing the target rock mass into a plurality of material points according to the parameter information, and constructing a thermal coupling model of the target rock mass;

[0010] Based on the initialized thermal-mechanical coupling model, time step iteration simulation of the solid mechanics field is performed, and finally the crack propagation process and temperature distribution of the target rock mass are obtained.

[0011] In each iteration time step, first, based on the physical field information of the current time step, the temperature of each material point is predicted using the neural network model 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, according to the updated physical field information, it is judged whether the bond is broken, and the micro-modulus 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 near-field dynamics control equation until the termination condition is triggered.

[0012] According to some embodiments, the present application adopts the technical scheme as follows:

[0013] The rock mass high-temperature deformation simulation system based on deep learning near-field dynamics comprises:

[0014] The information acquisition module is configured to acquire parameter information of a target rock mass to be simulated, including the geometric shape of the rock mass and the physical properties of the rock mass;

[0015] The model construction module is configured to discretize the target rock mass into a plurality of material points according to the parameter information, and construct a thermal-mechanical coupling model of the target rock mass;

[0016] The iteration simulation module is configured to, based on the initialized thermal-mechanical coupling model, perform time step iteration simulation of the solid mechanics field, and finally obtain the crack propagation process and temperature distribution of the target rock mass.

[0017] In each iteration time step, first, based on the physical field information of the current time step, the temperature of each material point is predicted using the neural network model 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, according to the updated physical field information, it is judged whether the bond is broken, and the micro-modulus 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 near-field dynamics control equation until the termination condition is triggered.

[0018] According to some embodiments, the present application adopts the technical scheme as follows:

[0019] A computer program product comprising a computer program which, when executed by a processor, implements the rock mass high-temperature deformation simulation method based on deep learning near-field dynamics.

[0020] According to some embodiments, the present application adopts the technical scheme as follows:

[0021] The application discloses a non-transitory computer readable storage medium for storing computer instructions, which, when executed by a processor, implement the deep learning based near-field dynamics rock mass high-temperature deformation simulation method.

[0022] According to some embodiments, the application adopts the technical scheme as follows:

[0023] An electronic device comprises a processor, a memory and a computer program; wherein the processor is connected with 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 deep learning based near-field dynamics rock mass high-temperature deformation simulation method.

[0024] Compared with the prior art, the application has the beneficial effects that:

[0025] (1) The application introduces a non-local differential operator, establishes a stress analysis solving model, incorporates the proposed strain energy density change formula into the near-field dynamics micro-modulus solving, establishes the correlation between the mechanical parameters of the medium at the crack and the residual strain energy, and can more accurately consider the influence of crack propagation on the mechanical properties of the material.

[0026] (2) The application effectively avoids the redundancy of traditional near-field dynamics heat conduction iterative calculation, and realizes fast temperature prediction in thermal force coupling simulation. The physical information neural network embeds physical laws into the training process, can efficiently obtain the temperature distribution in each solid time step, greatly reduces the calculation time and resource consumption, and improves the simulation efficiency.

[0027] (3) The application trains the near-field dynamics heat conduction result through the physical information neural network, can capture the complex nonlinear relationship of the thermal force coupling of fractured rock mass. Compared with the traditional method, the neural network model has stronger self-adaptive ability, can process complex scenes of different rock types and crack distribution, and improves the accuracy of the simulation result. BRIEF DESCRIPTION OF DRAWINGS

[0028] The drawings accompanying the specification of the application form a part of the application and serve to further understand the application, and the illustrative embodiments of the application and the description thereof are used to explain the application, and do not constitute an improper limitation on the application.

[0029] Figure 1 The deep learning based near-field dynamics rock mass high-temperature deformation simulation method flowchart of embodiment 1.

[0030] Figure 2 The near-field dynamics material point principle diagram in embodiment 1.

[0031] Figure 3A rock mass thermal conduction flowchart for the physical information neural network of Example 1 is shown in FIG. 1. DETAILED DESCRIPTION

[0032] The application is further described below in conjunction with the accompanying drawings and examples.

[0033] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0034] It should be noted that the terms used herein are only intended to describe specific embodiments and are not intended to limit exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should be understood that when the terms "comprise" and / or "comprises" are used in the specification, there is a reference to the presence of a feature, step, operation, device, component, and / or combinations thereof.

[0035] Physical information neural network (PINN) provides a new way to solve complex physical problems. PINN combines physical laws with neural networks, and can use a large amount of historical data to train the network, thereby capturing the complex relationship between input and output and providing an efficient solution. The present application combines PINN technology under the existing near-field dynamics framework, proposes a rock mass high temperature deformation simulation method and system based on deep learning near-field dynamics, and establishes a new deep learning near-field dynamics calculation framework for rock mass high temperature thermal-mechanical coupling, to overcome the shortcomings of the prior art and improve the accuracy and computational efficiency of near-field dynamics thermal-mechanical coupling simulation, which is widely applicable to the fields of geotechnical engineering, geothermal development, nuclear energy engineering, fire protection, etc.

[0036] Example 1

[0037] In one embodiment of the present application, a rock mass high temperature deformation simulation method based on deep learning near-field dynamics is provided, as shown in FIG. 1, which includes: Figure 1

[0038] Step 1: Obtain the parameter information of the target rock mass to be simulated, including the geometric shape of the rock mass and the physical properties of the rock mass;

[0039] Step 2: Discretize the target rock mass into a plurality of material points according to the parameter information, and construct a thermal-mechanical coupling model of the target rock mass;

[0040] Step 3: Based on the initialized thermal-mechanical coupling model, perform time step iteration simulation of the solid mechanics field, and finally obtain the crack propagation process and temperature distribution of the target rock mass;

[0041] ​Wherein, in each iteration time step, first, based on the physical field information of the current time step, the temperature of each material point is predicted by using the neural network model 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, according to the updated physical field information, it is judged whether the bond breaks or not, and the micro modulus 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 near-field dynamics control equation until the termination condition triggers.

[0042] As an embodiment, the rock mass high temperature deformation simulation method based on deep learning near-field dynamics of the application introduces the solid field near-field dynamics theory based on strain energy density, combines the fluid field near-field dynamics equation, predicts the temperature distribution in the rock medium through the physical information neural network, forms the deep learning near-field dynamics framework of rock mass high temperature deformation and failure, and thus efficiently and accurately simulates the rock mass high temperature deformation.

[0043] S1 introduces the solid field near-field dynamics theory based on strain energy density.

[0044] By introducing the solid field near-field dynamics theory based on strain energy density, the solid field near-field dynamics control equation and non-local force density are constructed.

[0045] Specifically, the stress calculation process in the solid field near-field dynamics theory is represented by the formula:

[0046] (1)

[0047] Wherein, the coordinates of the target material point are represented as , And is the component of the relative position vector , is an infinitesimal excess, the function is a known quantity, - is a change, is a partial differential symbol, and for two-dimensional analysis, the derivative can be calculated by formula (1):

[0048] (2)

[0049] Wherein, And are the functions For the derivatives of And , is The set of other interacting material points in the neighborhood of , that is, the neighborhood of the material point , for , The relative position vector, For two-dimensional spatial measurement, They are nonlocal orthogonal functions. and This corresponds to the order.

[0050] Furthermore, nonlocal orthogonal functions Satisfies the following orthogonality:

[0051] (3)

[0052] in, n 1. n 2. p 1. p 2 is the order of the orthogonal function expansion. ξ 1. ξ 2 represents the components of ξ in the two coordinate directions. and This is the Dirac function.

[0053] Furthermore, the near-field dynamic stress calculation in step S1 utilizes differential operators to represent the Navier equilibrium equations. In the two-dimensional case, the stress components can be constructed as follows:

[0054] (4)

[0055] (5)

[0056] (6)

[0057] In the formula, and These are the elastic modulus and Poisson's ratio of the material, respectively. and These represent displacements in two coordinate directions, respectively.

[0058] Thus, by introducing nonlocal differential operators, a stress analysis solution model represented by formulas (4)-(6) was established.

[0059] Furthermore, Figure 2 This is a schematic diagram of near-field dynamics of matter points, such as... Figure 2 As shown, Representing a point of matter The circular neighborhood, for Other interacting matter points in the neighborhood, The neighborhood radius, for The velocity at time t For , the relative position vector of the point, is the relative displacement of the point after shape change, based on the near-field dynamic point principle in Figure 2 , the solid field near-field dynamic control equation in step S1 and the non-local force density are respectively expressed as:

[0060] (7)

[0061] (8)

[0062] wherein, is the acceleration at the time, is the solid density, t is the body force at the point, is the force density of the classical near-field dynamics, represents the volume of the interaction point , , , are the positions after deformation, , respectively, , are the positions after deformation, is the relative displacement of the point after shape change, is the micro potential energy at the point, is the micro modulus of the model, is the elongation of the key.

[0063] The elongation and the strain energy density at the point are respectively expressed as:

[0064] (9)

[0065] (10) wherein,

[0066] is the volume of the interaction point , is the strain energy density at the point. W Further, S1 introduces the strain energy density theory to establish the nonlinear correspondence between the effective elastic modulus

[0067] at the crack tip of the rock in different dissipation stages and the residual strain energy . For the elastic stage, the elastic modulus is the same as the initial elastic modulus :

[0068] ​ (11)

[0069] Crack initiation and propagation stages:

[0070] (12)

[0071] Post-peak softening stage:

[0072] (13)

[0073] Residual stage:

[0074] (14)

[0075] in, It is the maximum value of the residual strain energy. This is the final value of the residual strain energy, where a and b are constants determined experimentally as positive numbers, typically b > a. This represents the residual effective elastic modulus.

[0076] The proposed strain energy density variation formula (i.e., formula 11-14) was incorporated into the solution of near-field dynamic micromodulus, establishing the correlation between the mechanical parameters of the medium at the crack and the residual strain energy.

[0077] Specifically, for two-dimensional analysis, the micromodulus can be determined based on the effective elastic modulus at different stages. :

[0078] (15)

[0079] in, For effective elastic modulus, The neighborhood radius, For thickness, Poisson's ratio, micromodulus As the loading process changes, the nonlocal force density is updated in real time. Therefore, equation (8) (i.e., the nonlocal force density) can be updated as follows:

[0080] (16)

[0081] in, For matter points , The relative position vectors between them This represents the relative displacement of a point in the material after its shape changes.

[0082] Nonlocal force density Subject to effective elastic modulus and elongation s The effective elastic modulus is determined by the residual strain energy at the calculation point, influenced by two factors. Sure.

[0083] Furthermore, matter points and The function for the bond breakage state is: When the function This indicates that the bond is not broken and there is a nonlocal force density, when the function When the bond breaks, the nonlocal force density disappears.

[0084] The degree of damage at point x is defined as:

[0085] (17)

[0086] when When x is broken, it means that all bonds at x are broken and the point is completely destroyed.

[0087] S2 constructs a near-field dynamic theory of temperature field diffusion in fractured rock masses;

[0088] Furthermore, in the near-field dynamics theory of the S2 temperature field, the heat conduction process occurs within a nonlocal influence domain of a certain size, and the material point... and The key between The channels considered as heat conduction are in t time heat flux for:

[0089] (18)

[0090] in, It is a relative position vector. rock material points and The macroscopic thermal conductivity between them Let be the temperature difference between two points of matter at time t. The unit direction vector of the bond in the reference coordinate system.

[0091] According to the law of conservation of thermal energy, the governing equation for near-field dynamic heat conduction is:

[0092] (19)

[0093] in, ρ For material density, c v For the specific heat capacity of the material, For matter points temperature, Generates heat per unit volume of external space. For nonlocal calculation of thermal conductivity of materials, it can be determined by the equivalent relationship between near-field dynamic heat flux and heat flux in traditional continuous medium theory. For two-dimensional analysis:

[0094] (20)

[0095] where, is the macroscopic thermal conductivity coefficient is a short form of is the neighborhood radius, is the thickness.

[0096] Further, in the process of rock thermal conduction, if the rock is broken, the thermal conduction mode in the crack is composite, in addition to the thermal conduction of the solid part of the rock, the heat can also be conducted through the medium in the crack. The difference in thermal conductivity of different media leads to obvious changes in the process of heat conduction. The effective thermal conductivity coefficient K eff The influence of the following factors is comprehensively considered:

[0097] (21)

[0098] where, dmg is the damage degree of the material point, is the macroscopic thermal conductivity coefficient, K M is the thermal conductivity coefficient of the medium at the crack, a R and b M are constants, which can be determined according to the test. If the crack is filled with water or other fluids, the conduction coefficient K M will increase, and the heat flow will spread along the crack, rather than simply along the solid part of the rock; if the crack is dry or filled with gas, the conduction coefficient will decrease.

[0099] In the calculation of thermal conduction, the average value of the thermal conductivity coefficient between and is taken:

[0100] (22)

[0101] where, and are the thermal conductivity coefficients of and , specifically the macroscopic thermal conductivity coefficient of the rock before breaking K R or the effective thermal conductivity coefficient K eff after breaking.

[0102] S3 establishes a physical information neural network to predict the temperature distribution in rock media;

[0103] Further, S3 establishes a physical information neural network to predict the temperature distribution in rock media, which includes an input layer, a hidden layer, and an output layer.

[0104] The input layer needs to fully describe the information of the material point and ensure that the input matches the output characteristics, and selects the spatial coordinate position x of the material point, the corresponding thermal conductivity K as input:

[0105] (23)

[0106] where sta () represents the standardization of input characteristics, and the thermal conductivity K includes the macroscopic thermal conductivity of the rock before rupture 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 characteristics.

[0107] Further, 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.

[0108] Further, all hidden layers use nonlinear activation functions, including but not limited to RELU, SELU, Sigmoid, Tanh, etc., and their activation functions can all perform the task of model training. Among them, the RELU activation function is relatively simple to calculate and can accelerate training:

[0109] (24)

[0110] When the input d is greater than 0, the output is d When the input d is less than or equal to 0, the output is 0. In addition, ReLU does not have the problem of gradient disappearance compared to Sigmoid, and is suitable for deep networks. The output layer is the temperature distribution T (x), which does not require a nonlinear activation function:

[0111] (25)

[0112] Further, to ensure the neural network can be trained effectively, the input thermal conductivity K is pre-processed properly, and the standardization (Z-Score Normalization) method which can accelerate the training effectively is selected. The method can ensure that all input data have the same dimension, thereby avoiding the instability of training caused by the large magnitude of some features:

[0113] (26)

[0114] wherein, K ave is the mean of the data, σ K is the standard deviation.

[0115] 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. For two-dimensional analysis, at the coordinates x 1and x 2, d x 1and d x 2are added respectively, and the original coordinates are transformed into (d x 1, x 2). x x Further, in the process of forward propagation before model training, the input data is calculated through the network layer to obtain the predicted value

[0116] , and the number of hidden layers of the neural network is L. The calculation of each layer is represented as:

[0117] (27)

[0118] wherein, l is the hidden layer, is the output of the hidden layer, and the output of each layer will be used as the input of the next layer. is the activation function (ReLU is used for the hidden layer, and linear activation is used for the output layer), and are the weight matrix and the bias vector in the l th layer.

[0119] Further, to ensure that the output of the neural network satisfies the physical constraints of the near-field dynamics equation, the residual L heat between the temperature predicted value and the true value is used as part of the loss term:

[0120] (28)

[0121] wherein, ​​With are the real and predicted temperature values of the i th material point, respectively, N is the total number of material points.

[0122] The boundary condition can be either a fixed temperature boundary condition (Dirichlet boundary condition) or a heat flux density boundary condition (Neumann boundary condition).

[0123] For Dirichlet boundary condition (given temperature value at a certain point), the loss function is expressed as:

[0124] (29)

[0125] For Neumann boundary condition (such as given heat flux density at a certain point), the loss function is expressed as:

[0126] (30)

[0127] where, L bd is the boundary condition loss term, where and are the real and predicted temperature values of the bd th material point at the boundary, respectively, N bc is the total number of boundary material points, is the real heat flux density on the boundary, is the gradient of temperature in the normal direction of the boundary.

[0128] Further, to ensure that the network can consider the heat flux transfer between material points when predicting the temperature distribution, an additional loss term is introduced to calculate the predicted heat flux between each pair of adjacent material points and compare it with the real heat flux , which is expressed by the formula:

[0129] (31)

[0130] (32)

[0131] where, L flux is the heat flux loss term, is the thermal conductivity coefficient between rock material points and , including the macroscopic thermal conductivity coefficient K R and the effective thermal conductivity coefficient K eff .

[0132] The total loss function of the physical information neural network is obtained by combining all the loss terms above L total :

[0133] (33)

[0134] Further, the back propagation is performed by calculating the gradient of the loss function with respect to each parameter and updating the parameters by the gradient descent method.

[0135] The gradients of the output layer and the hidden layer are respectively:

[0136] (34)

[0137] (35)

[0138] wherein, is the linear combination of the l layer, represents the gradient term, is the derivative of the activation function, and ⊙ represents element-wise multiplication.

[0139] The weight matrix and the bias vector are respectively:

[0140] (36)

[0141] In order to avoid constructing a complete derivative expression, AD automatic differentiation is used in the calculation of the gradient.

[0142] S4 forms a rock mass thermal-mechanical coupling deep learning near-field dynamics algorithm.

[0143] Further, in the S4 rock mass thermal-mechanical coupling deep learning near-field dynamics algorithm, the crack rock mass temperature distribution prediction model trained by S3 is incorporated into the near-field dynamics thermal-mechanical coupling calculation. In each solid mechanics field time step solution, the S3 prediction model is used to quickly obtain the temperature distribution of the crack rock mass, without the need for a large number of heat conduction iteration steps in the traditional dynamics method in S2, greatly improving the calculation efficiency.

[0144] Further, after quickly obtaining the temperature distribution of the rock mass, according to the thermal-mechanical coupling effect of the rock, the force density after coupling of the solid mechanics field can be expressed as:

[0145] (37)

[0146] wherein, α represents the thermal expansion coefficient of the rock material, and the near-field dynamics thermal-mechanical coupling equation of the strain energy density softening criterion under two-dimensional analysis can be obtained by combining equations (7) and (15):

[0147] (38)

[0148] The connection key fracture state function is updated with time step:

[0149] (39)

[0150] Wherein, s 0 is the critical value of key fracture, which is related to the critical energy release rate of rock, is is The average value of temperature, 0 and 1 represent the fracture and integrity of the key respectively.

[0151] Further, with the iterative calculation of the mechanical field, the fractured rock mass gradually damages, and the effective thermal conductivity coefficient changes according to formula (21), and the updated effective thermal conductivity coefficient is used in the next time step to predict the temperature distribution, and the newly predicted temperature distribution is fed back to formula (38) and (39), realizing the coupling process.

[0152] Embodiment 2

[0153] In an embodiment of the present application, a rock mass experiment verification process of a deep learning near-field dynamics-based rock mass high-temperature deformation simulation method is provided, a two-dimensional three-point bending rock beam is selected as a standard fracture test piece, which comprises:

[0154] 1. Test piece and discretization.

[0155] In this embodiment, a two-dimensional three-point bending rock beam is selected as a standard fracture test piece, and the geometric size is unified as follows: length L=0.20m, height h=0.05m, thickness t=0.01m. A I-shaped straight crack is pre-prepared in the middle of the beam bottom, and the initial crack length is 0.01m, so as to ensure that the crack tip is located in the pure bending area. The entire calculation domain is discretized by using uniform square grid, the spacing between material points is 1mm, and a total of 10000 material points are included; the neighborhood radius δ of each point is 3.015mm, which meets the convergence requirement of near-field dynamics, and also takes into account the calculation efficiency.

[0156] 2. Material parameters.

[0157] The initial elastic modulus of rock , Poisson's ratio v=0.3, and density . In order to describe the mechanical residual behavior after cracking, the key parameters of residual strain energy are introduced: , which reflects the upper limit of energy dissipation of the material in the crack propagation process, and is the residual strain energy density when the crack is completely destroyed; It reflects the residual energy of the material remaining in the crack tip after the crack propagation is completed. The empirical constants are determined by the indoor three-point bending test curve inversion, and a = 2.0, b = 3.5, and b > a are obtained.

[0158] 3. Real-time calculation of residual strain energy.

[0159] In the calculation process, the strain energy density of each material point W is directly calculated from the current micro-potential energy state:

[0160]

[0161] When the bond elongation s exceeds the critical value s 0, the energy begins to dissipate. The residual strain energy density is updated in an incremental accumulation manner.

[0162] 4. Stage updating.

[0163] The effective elastic modulus and the residual strain energy have a nonlinear correspondence. For the elastic stage, the elastic modulus is the same as the initial elastic modulus :

[0164]

[0165] Crack initiation and propagation stage:

[0166]

[0167] Post-peak softening stage:

[0168]

[0169] Residual stage:

[0170]

[0171] 5. Dynamic assignment of micro-modulus c.

[0172] Under the bond-based near-field dynamics framework, the micro-modulus of the material point is linearly related to the current effective elastic modulus:

[0173]

[0174] Therefore, when the crack tip enters the softening or residual stage, the effective elastic modulus rapidly decreases, resulting in the micro-modulus c synchronously decreasing, and the non-local force density automatically decreasing with the bond elongation, which macroscopically manifests as a rapid drop in bearing capacity, consistent with the test curve.

[0175] 6. Result verification.

[0176] When the loading displacement reaches 0.2mm, the residual strain energy density of the material point 1mm in front of the crack tip is measured . Compared with the local effective stiffness back calculated by the digital image correlation (DIC) test, the error is less than 5%; the crack propagation path is smooth and mesh-independent, which fully verifies the effectiveness and practicability of the nonlinear stiffness degradation model based on residual strain energy driving in the near-field dynamics simulation of fractured rock mass.

[0177] Embodiment 3

[0178] In an embodiment of the present application, the specific process of neural network model construction and training in the deep learning near-field dynamics-based rock mass high-temperature deformation simulation method is provided, taking a two-dimensional single-fracture sandstone plate as an object, as shown in Figure 3 , comprising:

[0179] 1. Overview.

[0180] In this embodiment, a two-dimensional single-fracture sandstone plate is taken as an object, with a geometric size of 0.4m x 0.2m, which is used to simulate a single-fracture granite temperature unit in underground rock mass. A straight fracture is preset in the plate, with a length of 0.1m and an inclination angle of 0 degrees, located at the center line of the plate. Different constant temperatures are applied to the left and right boundaries, and the upper and lower boundaries are set as adiabatic boundaries. The model is trained by a four-hidden-layer fully connected physical information neural network to realize high-precision mapping from “spatial coordinates + thermal conductivity” to “node temperature”, and then replace the traditional iterative temperature solving in subsequent thermal coupling calculation, significantly improving the calculation efficiency and ensuring the accuracy.

[0181] 2. Data preparation.

[0182] In order to obtain sufficient and physically credible training samples, the traditional near-field dynamics heat conduction solving is first used to generate a database. The specific steps are as follows:

[0183] (1) 10 levels of constant temperature conditions are combined for the left and right boundaries; 5 levels of thermal conductivity are taken for the rock matrix; and 5 levels of thermal conductivity are taken for the fracture filling medium.

[0184] (2) For each combination, steady-state calculation is performed, and 1mm uniform grid is used for discretization, with a total of about 80000 nodes. After the calculation is completed, the coordinates, current thermal conductivity and steady-state temperature are extracted at each node.

[0185] (3) The simulation results are divided into training set, validation set and test set according to the ratio of 8:1:1 to ensure statistical consistency. Z-Score normalization method is used to process the initial data.

[0186] (4) Randomly shift the coordinates and impose uniform noise on permeability to generate 20% extra samples for improving the robustness of the model.

[0187] 3. PINN network structure.

[0188] The network is a fully connected feedforward structure: 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; the output layer has 1 neuron with a linear activation. The weights are initialized using Xavier uniform initialization, and the bias is initialized to 0. To suppress overfitting, Dropout is added after hidden layer 2 and hidden layer 3 with a dropout probability of 0.05.

[0189] 3. Training configuration.

[0190] The total loss function is composed of three weighted terms: data loss, boundary loss, and heat flux loss. The empirical weights are determined by grid search. The training is divided into two stages: in the first stage, the Adam optimizer is used with a learning rate of 1e-3, a weight decay of 1e-4, a batch size of 4096, and a total of 5000 steps; in the second stage, the L-BFGS fine-tuning is switched to with a maximum of 1000 iterations. In the Adam stage, the learning rate is multiplied by 0.8 to decay every 1000 steps. Early stopping is monitored on the validation set, and if there is no improvement for 20 consecutive steps, the training is terminated. The training is completed on a single RTX-3070.

[0191] 4. Post-training validation.

[0192] 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 region; coefficient of determination , indicating that the network has good generalization ability.

[0193] Example 4

[0194] In one embodiment of the present application, a specific embodiment of a rock mass high-temperature deformation simulation method based on deep learning near-field dynamics is provided, which includes:

[0195] 1. Region construction. Initialize the calculation domain, input the geometric size of the rock mass, the position of the crack, and assign the density, elastic modulus, Poisson's ratio, specific heat capacity, thermal expansion coefficient, and thermal conductivity of the rock mass matrix and crack medium; calculate and store the effective thermal conductivity according to the crack damage state to form a thermal property field that can evolve with damage.

[0196] 2. Initialization of calculation parameters. Set the total number of material points, neighborhood radius, initial displacement, initial temperature, boundary condition type and value; generate all material point coordinates and establish an adjacency list; assign each key an initial micro-modulus, initial fracture state and initial non-local force; set the time step length, total calculation time and data output frequency.

[0197] 3. Deployment of prediction model. Load the trained crack rock mass temperature distribution prediction model in a callable form; bind the current material point coordinates and effective thermal conductivity coefficient to the input interface; the output interface directly returns the temperature values of each material point without additional format conversion.

[0198] 4. Thermal-mechanical coupling time marching. At the beginning of each solid mechanics field time step, call the prediction model to obtain the global temperature distribution at one time; pass the obtained temperature field to the solid mechanics solver; calculate the thermal stress according to the temperature increment and update the non-local force density; solve the material point acceleration, velocity and displacement by executing the near-field dynamics motion equation; judge whether the key is broken according to the key elongation, and if broken, update the damage variable and effective thermal conductivity coefficient.

[0199] Example 5

[0200] In an embodiment of the present application, a specific embodiment of a rock mass high temperature deformation simulation method based on deep learning near-field dynamics is provided, comprising:

[0201] A1. Construction of solution region;

[0202] A2. Initialization of calculation parameters;

[0203] A3. Training of prediction model;

[0204] A4. Thermal-mechanical coupling simulation;

[0205] A5. Result analysis.

[0206] Further, the main content of A1. Construction of solution region is: initialize the solution domain, define the geometry of the fractured rock mass, including the thickness, length, crack distribution and other parameters of the rock mass; set the physical properties of the rock mass, such as the elastic modulus, Poisson's ratio, density, specific heat capacity, thermal conductivity coefficient, etc., determine the effective thermal conductivity coefficient from the crack damage area to ensure that the solution model can truly reflect the thermal-mechanical coupling behavior of the rock mass.

[0207] Further, the A2 calculation parameter initialization mainly includes: setting calculation parameters according to the structural characteristics of the fractured rock mass, including the number of material points, the neighborhood radius, the boundary condition and other information; configuring non-local differential operators, key micro-modulus, strain energy density, non-local calculation 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 in the field of each material point; initializing the key, non-local force of the material point in its near-field field, and initializing the displacement, temperature and other information of the material point.

[0208] Further, the A3 prediction model training mainly includes: using the numerical results of the near-field dynamics thermal conduction simulation as the training set, changing various boundary conditions and initial damage states to increase the number of training sets, and dividing the test set; normalizing the thermal conductivity coefficient data, determining the network structure and initializing the weights and biases; inputting the training set data into the neural network, calculating the predicted value and loss function value through forward propagation; updating the weights and biases of the neural network using automatic differentiation according to the loss function value, and performing back propagation; repeating the above process until the total loss function converges or the preset training number is reached; using the test set data to evaluate the final performance of the model, and adjusting the network structure if the model performance is poor.

[0209] Further, the A4 thermal-mechanical coupling simulation mainly includes: deploying the trained temperature prediction model to carry out thermal-mechanical coupling simulation of the fractured rock mass; in each iteration time step of the solid mechanics field, the temperature of the material point is directly obtained using the neural network model; the non-local force, acceleration, displacement, stress and other information of each material point are calculated, and if the elongation rate is greater than the critical damage elongation rate, the key non-local force between the material points disappears, and the damage and effective thermal conductivity coefficient are updated; then the updated information is fed back to the prediction model, and the temperature of the material point in the next iteration time step is obtained, realizing coupled calculation until the calculation termination condition is triggered.

[0210] Further, the A5 result analysis mainly includes: outputting the thermal-mechanical coupling simulation results of the fractured rock mass, visualizing and analyzing the crack propagation process and temperature distribution of the rock mass.

[0211] Embodiment 6

[0212] In an embodiment of the present application, a rock mass high-temperature deformation simulation system based on deep learning near-field dynamics is provided, which comprises:

[0213] The information acquisition module is configured to acquire parameter information of a target rock mass to be simulated, including the geometric shape of the rock mass and the physical properties of the rock mass;

[0214] The model construction module is configured to discretize the target rock mass into a plurality of material points according to the parameter information, and construct a thermal-mechanical coupling model of the target rock mass;

[0215] iteratively simulate the time step of the solid mechanics field based on the initialized thermal-mechanical coupled model, and finally obtain the crack propagation process and temperature distribution of the target rock mass;

[0216] In each iteration time step, first, based on the physical field information of the current time step, the temperature of each material point is predicted by using the neural network model to obtain the temperature distribution of the current time step; then, the physical field information is updated according to the thermal-mechanical coupling effect of the rock; secondly, the key is judged whether to break according to the updated physical field information, and the micro-modulus and non-local force density are updated based on the judgment result; finally, the physical field information is updated by the near-field dynamics control equation based on the non-local force density until the termination condition is triggered.

[0217] Embodiment 7

[0218] In an embodiment of the present application, a computer program product is provided, comprising a computer program, which, when executed by a processor, implements the deep learning near-field dynamics based rock mass high temperature deformation simulation method.

[0219] Embodiment 8

[0220] In an embodiment of the present application, a non-transitory computer readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the deep learning near-field dynamics based rock mass high temperature deformation simulation method.

[0221] Embodiment 9

[0222] In an embodiment of the present application, an electronic device is provided, comprising a processor, a memory and a computer program; wherein the processor is connected with 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 deep learning near-field dynamics based rock mass high temperature deformation simulation method.

[0223] The present application is described with reference to flowcharts and / or block diagrams of the method, device (system) and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be realized by computer program instructions. These computer program instructions can be provided to the 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 realize the functions described in the flowcharts and / or block diagrams. Figure 1 one flow or multiple flows and / or blocks Figure 1means for performing the function specified by the block or blocks.

[0224] These computer program instructions can also be loaded into computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable data processing devices to generate a computer implemented process, so that the instructions executed on the computer or other programmable data processing devices provide a process for implementing the flowchart Figure 1 flowchart or flowcharts and / or block Figure 1 steps of a function specified by a block or blocks.

[0225] The above description is made in connection with the preferred embodiments of the application, and is not intended to limit the scope of the application. Those skilled in the art should understand that various modifications or variations can be made to the technical solutions of the application without departing from the spirit and scope of the application, and these modifications or variations should still fall within the protection scope of the application.

Claims

1. A method for high-temperature deformation simulation of rock mass based on deep learning near-field dynamics, characterized in that, The method comprises the following steps: obtaining parameter information of a target rock mass to be simulated, including the geometric shape of the rock mass and the physical properties of the rock mass; discretizing 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; the thermal-mechanical coupling model is constructed by introducing a solid field near-field dynamics theory based on strain energy density, combining a fluid field near-field dynamics equation, and constructing a near-field dynamics thermal-mechanical coupling equation of a strain energy density softening criterion; based on the initialized thermal-mechanical coupling model, performing time step iteration simulation of the solid mechanics field, and finally obtaining the crack propagation process and temperature distribution of the target rock mass; wherein, in each iteration time step, first, based on the physical field information of the current time step, the temperature of each material point is predicted by using a neural network model 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, according to the updated physical field information, it is judged whether the key breaks or not, and the micro modulus 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 near-field dynamics control equation until the termination condition is triggered.

2. The deep learning based near-field dynamics based rock mass high temperature deformation simulation method of claim 1, wherein, The geometric shape includes the thickness, length and fracture distribution of the rock mass; the physical properties include the elastic modulus, Poisson's ratio, density, specific heat capacity and thermal conductivity coefficient of the rock mass.

3. The deep learning based near-field dynamics based rock mass high temperature deformation simulation method of claim 1, wherein, The neural network model adopts a physical information neural network (PINN), takes the physical field information of the material point as input, and takes the temperature value of the material point as output; wherein the physical field information includes coordinates and effective thermal conductivity coefficient.

4. The deep learning based near-field dynamics based rock mass high temperature deformation simulation method of claim 1, wherein, According to the thermal-mechanical coupling effect of the rock, the physical field information is updated, specifically: calculate the thermal stress according to the temperature increment, update the non-local force density, and execute the fluid field near-field dynamics equation to solve the physical field information of the material point.

5. The deep learning based near-field dynamics based rock mass high temperature deformation simulation method of claim 1, wherein, According to the updated physical field information, it is judged whether the key breaks or not, and the micro modulus and non-local force density are updated based on the judgment result, specifically: judge the fracture state based on the elongation between two material points; if fracture occurs, calculate the damage degree, and calculate the residual strain energy and micro modulus of the material point based on the damage degree; update the non-local force density according to the elongation and the effective elastic modulus in the micro modulus.

6. A rock mass high temperature deformation simulation system based on deep learning near-field dynamics, characterized in that, The method comprises the following steps: an information acquisition module configured to obtain parameter information of a target rock mass to be simulated, including the geometric shape of the rock mass and the physical properties of the rock mass; a model construction module configured to discretize the target rock mass into a plurality of material points according to the parameter information, and construct a thermal-mechanical coupling model of the target rock mass; the thermal-mechanical coupling model is constructed by introducing a solid field near-field dynamics theory based on strain energy density, combining a fluid field near-field dynamics equation, and constructing a near-field dynamics thermal-mechanical coupling equation of a strain energy density softening criterion; an iteration simulation module configured to perform time step iteration simulation of the solid mechanics field based on the initialized thermal-mechanical coupling model, and finally obtain the crack propagation process and temperature distribution of the target rock mass; In each iteration time step, first, based on the physical field information of the current time step, the temperature of each material point is predicted by using the neural network model 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, according to the updated physical field information, it is judged whether the bond is broken or not, and the micro-modulus 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 near-field dynamics control equation until the termination condition is triggered.

7. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to implement the deep learning near-field dynamics based rock mass high temperature deformation simulation method of any one of claims 1-5.

8. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium is used to store computer instructions, and the computer instructions are executed by the processor to implement the deep learning near-field dynamics based rock mass high temperature deformation simulation method of any one of claims 1-5.

9. An electronic device, comprising: Comprise: A processor, a memory and a computer program; wherein the processor is connected with 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 deep learning near-field dynamics based rock mass high temperature deformation simulation method of any one of claims 1-5.

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