Nonlinear finite element method and system for determining critical stability section of underground cavern

Abstract

This invention provides a nonlinear finite element method for determining the critical stability section of an underground cavern. Based on rock mechanics tests in actual engineering, the rock mass strain softening parameters are determined. A secondary development of the rock mass constitutive model is performed based on these parameters. An initial nonlinear finite element model for solving the critical stability section of the underground cavern is constructed based on the secondary developed rock mass constitutive model. The nonlinear finite element model is solved to obtain the overall tangential stiffness of the model at the calculation step. Based on the overall tangential stiffness, the minimum eigenvalue of the overall tangential stiffness matrix is ​​calculated. Based on the minimum eigenvalue, the critical stability section of the underground cavern is determined. This invention directly and quantitatively reflects the essential characteristics of stiffness loss and bearing capacity reduction in the entire cavern structure system after considering complex nonlinear deformation paths, including strain softening, thereby accurately capturing the critical instability moment and potential instability sections.

Description

Technical Field

[0001] This invention relates to the field of underground cavern cross-sectional stability discrimination technology, and particularly to a nonlinear finite element discrimination method for critical stability cross-sections of underground caverns. Background Technology

[0002] The stability criteria for the cross-section of underground caverns generally include the displacement mutation criterion, the plastic zone continuity criterion, and the safety factor criterion.

[0003] Among these methods, the displacement mutation criterion is the most widely used and has been incorporated into deformation control standards for underground cavern construction in various industries. This method relies on a sudden increase in displacement (velocity or magnitude) at monitoring points to determine the stability of the surrounding rock. In actual engineering, displacement mutations often occur after instability. Therefore, predicting the critical or ultimate displacement of the cavern failure process during design and construction is difficult, and its judgment is limited by factors such as cavern shape and measuring point location. In numerical simulations, the elastic modulus is most sensitive to displacement. However, the elastic modulus of rock mass is not easy to measure and can only be estimated using empirical formulas, which is highly subjective.

[0004] The plastic zone penetration criterion is mainly used in numerical simulation during the design process of the stratigraphic structure method. Its advantage is that the mechanical principle is simple and intuitive, but its disadvantage is also obvious. Yielding at a single point does not mean the loss of the bearing capacity of the surrounding rock, and the penetration of the plastic zone does not mean that failure has occurred.

[0005] The safety factor criterion is based on the finite element strength reduction method, which simulates the progressive failure process of slopes by gradually reducing the strength parameters of the soil and rock mass (mainly cohesion c and internal friction angle φ), and uses the strength reduction factor at failure as the safety factor. It often combines methods such as calculation non-convergence, abrupt displacement of characteristic points, plastic zone penetration, and ultimate strain to determine the failure surface of the tunnel.

[0006] Some studies have attempted to use constitutive models that reflect strain softening in numerical analysis (such as piecewise linear softening and plastic damage models). These models can more realistically simulate the softening process, but their stability criteria still rely on traditional methods (such as convergence, plastic zone, and displacement mutation), lacking an essential criterion that has a direct and quantitative mathematical connection with the decrease in structural load-bearing capacity caused by the softening process.

[0007] In summary, the core problem with existing technologies is the lack of a nonlinear finite element analysis method that closely integrates a constitutive model of strain softening in complex rock masses, accurate instability criteria, and can effectively locate critical cross-sections. Summary of the Invention

[0008] The present invention aims to solve at least one of the technical problems existing in the prior art, and proposes a nonlinear finite element discrimination method and system for the critical stability section of underground caverns.

[0009] In a first aspect, embodiments of the present invention provide a nonlinear finite element method for determining the critical stability section of an underground cavern, including:

[0010] Determine the rock mass strain softening parameters based on rock mechanics tests in actual engineering projects;

[0011] The constitutive model of the rock mass is further developed based on the aforementioned rock mass strain softening parameters;

[0012] Based on the constitutive model of the rock mass after secondary development, an initial nonlinear finite element model is constructed to solve the critical stability section of the underground cavern.

[0013] The nonlinear finite element initial model is solved to obtain the overall tangential stiffness of the model at the corresponding time step;

[0014] Based on the overall tangent stiffness, the minimum eigenvalue of the overall tangent stiffness matrix is ​​calculated;

[0015] Based on the minimum eigenvalue, the critical stability section of the underground cavern is determined.

[0016] Furthermore, the rock mass strain softening parameters are the rock mass parameters when the strength gradually decreases as the strain increases after the rock mass material reaches its peak strength, including at least the softening modulus and residual strength.

[0017] Furthermore, based on triaxial tests of rock mass in actual engineering projects, the rock mass strain softening parameters are determined. The specific methods include: obtaining the stress-plastic strain curve of the actual engineering project based on the triaxial tests of rock mass in actual engineering projects, and performing linear, exponential, or piecewise softening fitting on the stress-plastic strain curve to obtain the rock mass strain softening parameter function.

[0018] Furthermore, the rock mass constitutive model is further developed based on the rock mass strain softening parameters. The specific methods include: obtaining the range of rock mass that affects the stability of the underground cavern section, using the basic rock mass constitutive model provided in the user material subroutine module of the finite element solver for secondary development, importing the rock mass strain softening parameters into the original constitutive model, and obtaining a rock mass constitutive model that conforms to the actual engineering situation.

[0019] Furthermore, based on the constitutive model of the rock mass after secondary development, a nonlinear finite element initial model of the critical stability section of the underground cavern is constructed. Specific methods include:

[0020] Based on the actual excavation conditions of the underground cavern, a finite element model of the underground engineering was constructed, including the cavern geometry, excavation steps, and initial geostress field. The model was meshed using transition mesh technology, and corresponding parameters and boundary conditions were set.

[0021] Furthermore, the nonlinear finite element model is solved to obtain the global tangent stiffness at each calculation step. Specific methods include: directly obtaining the global tangent stiffness matrix using a nonlinear finite element solver; when the nonlinear finite element solver cannot directly obtain the global tangent stiffness matrix, automatically extracting the global tangent stiffness matrix under the current state using a developed script; real-time monitoring of the plastic zone area or feature point displacement of the model; and when the plastic zone area or displacement exceeds a preset threshold, starting the extraction of the tangent stiffness matrix for each subsequent calculation step.

[0022] Furthermore, based on the overall tangent stiffness, the minimum eigenvalue of the overall tangent stiffness matrix is ​​calculated. The specific method includes: calling the eigenvalue solver to solve for the eigenvalue of the overall tangent stiffness matrix at each iteration step, and sorting all the eigenvalues ​​from smallest to largest to obtain the minimum eigenvalue.

[0023] Furthermore, based on the aforementioned minimum eigenvalue, the critical stability section of the underground cavern is determined, specifically through the following methods:

[0024] The minimum eigenvalue is compared with the value 0. When the minimum eigenvalue is greater than or equal to 0, the cavern at that time step is in a stable state. The minimum eigenvalue at the next time step is calculated. If the minimum eigenvalue after traversing the overall tangent stiffness matrix of all calculation time steps is greater than or equal to 0, it indicates that the initial cavern shape is in a self-stable state. At this time, the initial nonlinear finite element calculation model of the critical stability section of the underground cavern needs to be adjusted, and the above steps are repeated until the minimum eigenvalue is less than 0. When the minimum eigenvalue is less than 0, the cavern at that time step is unstable, and the corresponding cavern section state is marked as the critical section state, generating an underground cavern early warning signal.

[0025] Secondly, this invention also discloses a nonlinear finite element discrimination system for the critical stability section of an underground cavern, comprising: a rock mass strain softening parameter determination unit, a rock mass constitutive model secondary development unit, an initial model construction unit for solving the critical stability section of the underground cavern, an overall tangential stiffness acquisition unit, a minimum eigenvalue calculation unit, and a critical stability section discrimination unit; wherein:

[0026] The rock mass strain softening parameter determination unit is used to determine the rock mass strain softening parameters based on rock mechanics tests in actual engineering projects.

[0027] The rock mass constitutive model secondary development unit is used to perform secondary development of the rock mass constitutive model based on the rock mass strain softening parameters;

[0028] The initial model building element for solving the critical stability section of underground caverns is used to construct the nonlinear finite element initial model of the critical stability section of underground caverns based on the constitutive model of the rock mass after secondary development.

[0029] The overall tangent stiffness acquisition unit is used to solve the nonlinear finite element model and obtain the overall tangent stiffness of the model.

[0030] The minimum eigenvalue calculation unit is used to calculate the minimum eigenvalue of the overall tangent stiffness matrix based on the overall tangent stiffness.

[0031] The critical stability section discrimination unit is used to discriminate the critical stability section of the underground cavern based on the minimum characteristic value.

[0032] Thirdly, the present invention also discloses an electronic device, comprising:

[0033] One or more processors;

[0034] Memory, used to store one or more programs;

[0035] When the one or more programs are executed by the one or more processors, the one or more processors implement the discrimination method.

[0036] This invention provides a nonlinear finite element method for determining the critical stability section of an underground cavern. Based on rock mechanics tests in actual engineering, the rock mass strain softening parameters are determined. A secondary development of the rock mass constitutive model is performed based on these parameters. An initial nonlinear finite element model for solving the critical stability section of the underground cavern is constructed based on the secondary developed rock mass constitutive model. The nonlinear finite element model is solved to obtain the overall tangential stiffness. Based on the overall tangential stiffness, the minimum eigenvalue of the overall tangential stiffness matrix is ​​calculated. Based on the minimum eigenvalue, the critical stability section of the underground cavern is determined. This invention utilizes the rigorous mathematical properties of the minimum eigenvalue to directly and quantitatively reflect the essential characteristics of stiffness loss and bearing capacity reduction in the entire cavern structure system after considering complex nonlinear deformation paths, including strain softening, thereby accurately capturing the critical instability moment and potential instability sections. Attached Figure Description

[0037] Figure 1 A flowchart illustrating a nonlinear finite element method for determining the critical stability section of an underground cavern, provided in an embodiment of the present invention.

[0038] Figure 2 A structural block diagram of a nonlinear finite element discrimination system for critical stability sections of underground caverns provided in an embodiment of the present invention;

[0039] Figure 3 This is a structural block diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0040] To enable those skilled in the art to better understand the technical solutions of the present invention, exemplary embodiments of the present invention are described below in conjunction with the accompanying drawings, including various details of the embodiments of the present invention to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0041] Where there is no conflict, the various embodiments of the present invention and the features thereof may be combined with each other.

[0042] As used herein, the term “and / or” includes any and all combinations of one or more related enumerated entries.

[0043] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used herein, the singular forms “a” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that when the terms “comprising” and / or “made of” are used in this specification, the presence of the stated feature, integral, step, operation, element, and / or component is specified, but the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof is not excluded. Terms such as “connected” or “linked” are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect.

[0044] Unless otherwise specified, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art. It will also be understood that terms such as those defined in commonly used dictionaries should be interpreted as having the meaning consistent with their meaning in the context of the relevant art and the invention, and will not be interpreted as having an idealized or overly formal meaning unless expressly so defined herein.

[0045] To address at least one of the technical problems existing in the aforementioned related technologies, this invention provides a nonlinear finite element method and system for determining the critical stability section of underground caverns.

[0046] This implementation discloses a nonlinear finite element method for determining the critical stability section of an underground cavern, such as... Figure 1 ,include:

[0047] S100. Based on rock mechanics tests in actual engineering projects, determine the rock mass strain softening parameters. In this embodiment, the rock mass strain softening parameters are the rock mass parameters when the strength gradually decreases as the strain increases after the rock material reaches its peak strength, including at least the softening modulus and residual strength. In this embodiment, the rock mass strain softening parameters are determined based on rock mechanics tests in actual engineering projects. The specific method includes: obtaining the stress-plastic strain curve in actual engineering projects based on uniaxial, triaxial, or shear tests of the rock mass, and performing linear softening fitting on the stress-plastic strain curve to obtain the rock mass strain softening parameters.

[0048] Specifically, in this embodiment, the determination of the strain softening parameters is based on the actual stress-plastic strain curve law under rock mechanics tests in actual engineering. A function of softening parameters (such as softening modulus and residual strength) is fitted, which can be linear softening, exponential softening, piecewise softening, or internal variables (equivalent plastic strain, plastic work, etc.). Furthermore, a database of relevant parameters is established to associate with various rock mass types in deep underground spaces (such as granite / sandstone, etc.) for easy retrieval.

[0049] The purpose of rock mechanics testing is to simulate the actual stress state of rocks deep underground (such as triaxial compression and shear) in the laboratory, thereby determining the strength, deformation, and failure characteristics of rocks under various stress conditions. Rock mechanics testing is a standard experimental method for revealing the mechanical behavior of rocks under different confining pressures. By simulating the stress environment deep underground, it provides us with crucial parameters indispensable for engineering design and safety assessments of major projects such as hydropower, mining, and tunnels, such as cohesion c, internal friction angle φ, elastic modulus E, Poisson's ratio u, and tangential stiffness k.

[0050] S200. Secondary development of the rock mass constitutive model based on the rock mass strain softening parameters; In this embodiment, the secondary development of the rock mass constitutive model based on the rock mass strain softening parameters includes: using the rock mass constitutive model built into the user material subroutine module in the finite element solver, secondary development of the constitutive model is carried out, and the rock mass strain softening parameters are imported into the constitutive model to obtain a rock mass constitutive model that conforms to the actual engineering situation.

[0051] Specifically, the user material subroutine module in the finite element solver can be used to further develop or modify the constitutive model of the rock mass during the strain softening stage. To improve computational efficiency, constitutive models that consider strain softening can be assigned to rock masses within the main excavation influence range (such as 3 times the tunnel diameter, or the potential failure area around the tunnel).

[0052] Specifically, in Finite Element Analysis (FEA), the User Material Subroutine (UMAT / VUMAT, etc., naming varies depending on the solver) is one of the core extension modules. Its core function is to allow users to define the constitutive relations (i.e., stress-strain relations) of materials, thereby overcoming the limitations of the built-in material models of general-purpose finite element solvers (such as Abaqus, ANSYS, LS-DYNA) and meeting the simulation needs of special materials (such as hyperelastic materials, composite materials, and phase change materials) or complex mechanical behaviors (such as elastoplasticity, viscoelasticity, and damage evolution). However, while general-purpose finite element solvers have hundreds of built-in classical material models (such as linear elasticity, ideal elastoplasticity, Drucker-Prager models, etc.), they cannot cover all engineering scenarios. At this point, the User Material Subroutine becomes a "bridge": it embeds the user-written custom constitutive logic into the finite element calculation process through the interface specifications reserved by the solver, realizing the combination of "general solver framework + custom material model". In this embodiment, the rock mass strain softening parameters are input into the rock mass constitutive model for secondary development.

[0053] S300. Based on the constitutive model of the rock mass after secondary development, a nonlinear finite element initial model is constructed to solve the critical stability section of the underground cavern;

[0054] In this embodiment, based on the secondary-developed rock mass constitutive model, a nonlinear finite element initial model for solving the critical stability section of underground caverns is constructed. The specific method includes:

[0055] Based on the actual excavation conditions of the underground cavern, an underground engineering finite element model is constructed, which includes the cavern geometry, excavation steps, and initial geostress field. The rock mass constitutive model is imported into the underground engineering finite element model, and the model is meshed using transition mesh technology, with corresponding parameters and boundary conditions set.

[0056] Specifically, a two-dimensional (or three-dimensional) finite element model of the underground engineering project is constructed, including the cavern geometry, excavation steps, and initial geostress field. Elements are divided, constitutive model values ​​are assigned, and boundary conditions are set. The model can be circular, horseshoe-shaped, or other cave shapes. This embodiment focuses on the method for determining the critical stability section based on nonlinear finite element methods, which is applicable to any initial cave shape. A transition mesh technique is used to refine the perimeter region of the cave (minimum element size = 0.1D, where D is the cave diameter) to reduce the number of elements in the non-affected zone.

[0057] S400. Solve the nonlinear finite element model to obtain the overall tangential stiffness of the model; In this embodiment, the nonlinear finite element model is solved to obtain the overall tangential stiffness of the model in the calculation step. The specific method includes: performing step-by-step iterative solution through nonlinear finite element to obtain the tangential stiffness matrix of the model in the current iteration step. In order to reduce the storage workload of the model tangential stiffness matrix, the increase of the plastic zone area or feature point displacement within the influence range of the cavern excavation in the model is monitored in real time. When the plastic zone area or displacement is greater than the preset trigger condition, the tangential stiffness matrix of each subsequent calculation step is extracted.

[0058] Typically, conditions are set to trigger the extraction of the global tangent stiffness matrix. For example, calculations are only performed when the plastic development of elements within the potentially affected area (such as one time the equivalent diameter of the excavation section) exceeds a certain proportion (50%-80%), or when the displacement rate increases significantly (1.5-2 times). This avoids extracting and storing the matrix at every step, saving time and improving computational efficiency.

[0059] Typically, finite element method solvers do not provide direct access to the global tangent stiffness matrix in real time through their user interfaces. This is the primary technical obstacle to implementing this method. During the solution process (usually at the end of each increment step and after iteration convergence), the global tangent stiffness matrix K for the current state needs to be automatically extracted using a developed script (such as a Python API based on a solver). T .

[0060] In this embodiment, S400 implements the key steps of this embodiment. Typically, the nonlinear finite element solver assembles the current stiffness matrix in each iteration step based on the current stress-strain state and constitutive relation (tangent modulus). It is necessary to accurately understand how the solver generates and updates the global tangent stiffness matrix K in the implicit analysis. T This mechanism allows for accurate acquisition of the extracted global tangent stiffness matrix K. T These are typically large sparse matrices. Efficient memory management and data storage / retrieval strategies are required to handle models that may contain tens of thousands of degrees of freedom.

[0061] S500. Based on the overall tangent stiffness, calculate the minimum eigenvalue of the overall tangent stiffness matrix; In this embodiment, based on the overall tangent stiffness, the minimum eigenvalue of the overall tangent stiffness matrix is ​​calculated. The specific method includes: calling the eigenvalue calculation solver to solve for the eigenvalue of the overall tangent stiffness matrix at each iteration step, and sorting all the eigenvalues ​​from smallest to largest to obtain the minimum eigenvalue.

[0062] Specifically, for the extracted large sparse symmetric matrix K TIt calls efficient sparse eigenvalue solver libraries (such as ARPACK), uses secondary development programming to open up the calling interface, and realizes automatic extraction and solving.

[0063] S600. Based on the minimum eigenvalue, the critical stability section of the underground cavern is determined. In this embodiment, the critical stability section of the underground cavern is determined based on the minimum eigenvalue. The specific method includes: comparing the minimum eigenvalue with the value 0. When the minimum eigenvalue ≥ 0, the cavern at that time step is in a stable state. The minimum eigenvalue at the next time step is calculated. If the minimum eigenvalue after traversing the overall tangent stiffness matrix of all calculation time steps is greater than or equal to 0, it indicates that the initial cavern shape is in a self-stable state and there will be no instability. At this time, the nonlinear finite element initial calculation model of the critical stability section of the underground cavern in S300 needs to be adjusted (adjusting the width, diameter, sag ratio, etc.), and the above steps are repeated until the minimum eigenvalue is less than 0. When the minimum eigenvalue is less than 0, the cavern at that time step is unstable, and the corresponding cavern section state is marked as the critical section state, generating an underground cavern early warning signal.

[0064] Specifically, in numerical calculations, due to computer rounding errors and approximations in the solution, the calculated minimum eigenvalue λmin may be a very small negative number, but its absolute value is much smaller than the order of magnitude of typical eigenvalues. A reasonable negative threshold needs to be set. When λmin ≤ ϵ (a small positive number, infinitely close to 0, such as 1e-6 to 1e-10) or |dλmin / d(step)| (the minimum λ increment with iteration), the system is considered unstable, thus distinguishing between true instability and numerical noise. Simultaneously, the moment λmin changes from positive to negative (or crosses the set negative threshold) corresponds to the critical point at which the cross-section of the underground cavern transitions from a stable / metastable state to an unstable state. This is an earlier and more theoretical precursor to instability than the breakthrough of the plastic zone or a sudden displacement.

[0065] In some preferred embodiments, after obtaining the minimum eigenvalue λmin at the critical point when the underground cavern cross-section transitions from a stable / metastable state to an unstable state, the minimum eigenvalue λmin is further verified. First, theoretical verification is performed, applied to simple models with analytical solutions or known solutions (such as plane strain circular caverns) to verify the accuracy of the λmin criterion and the rationality of the critical cross-section location. Then, a physical model test is conducted for comparison: the results are compared with those of a laboratory physical model (such as a geomechanical model test) to examine the method's ability to predict the actual instability process and failure surface.

[0066] This embodiment provides a nonlinear finite element method for determining the critical stability section of an underground cavern. Based on triaxial tests of rock mass in actual engineering, the rock mass strain softening parameters are determined. A secondary development of the rock mass constitutive model is performed based on these parameters. An initial finite element model for solving the nonlinearity of the critical stability section of the underground cavern is constructed based on the secondary developed rock mass constitutive model. The nonlinear finite element model is solved to obtain the overall tangential stiffness. Based on the overall tangential stiffness, the minimum eigenvalue of the overall tangential stiffness matrix is ​​calculated. The critical stability section of the underground cavern is determined based on the minimum eigenvalue. This invention utilizes the rigorous mathematical properties of the minimum eigenvalue to directly and quantitatively reflect the essential characteristics of stiffness loss and bearing capacity reduction in the entire cavern structure system after considering complex nonlinear deformation paths, including strain softening, thereby accurately capturing the critical instability moment and potential instability sections.

[0067] Based on the same inventive concept, embodiments of the present invention also provide a nonlinear finite element discrimination system for the critical stability section of underground caverns, such as... Figure 2 It includes: a rock mass strain softening parameter determination unit, a rock mass constitutive model secondary development unit, an underground cavern critical stability section construction unit, an overall tangential stiffness acquisition unit, a minimum eigenvalue calculation unit, and a critical stability section discrimination unit; among which:

[0068] The rock mass strain softening parameter determination unit is used to determine the rock mass strain softening parameters based on rock mechanics tests in actual engineering projects.

[0069] The rock mass constitutive model secondary development unit is used to perform secondary development of the rock mass constitutive model based on the rock mass strain softening parameters;

[0070] The initial model building element for solving the initial cross-section of the underground cavern is used to construct a nonlinear finite element initial model for solving the critical stability cross-section of the underground cavern based on the constitutive model of the rock mass after secondary development.

[0071] The overall tangent stiffness acquisition unit is used to solve the nonlinear finite element model and obtain the overall tangent stiffness of the model.

[0072] The minimum eigenvalue calculation unit is used to calculate the minimum eigenvalue of the overall tangent stiffness matrix based on the overall tangent stiffness.

[0073] The critical stability section discrimination unit is used to discriminate the critical stability section of the underground cavern based on the minimum characteristic value.

[0074] The specific working methods of the rock mass strain softening parameter determination unit, the rock mass constitutive model secondary development unit, the underground cavern critical stability section construction unit, the overall tangential stiffness acquisition unit, the minimum eigenvalue calculation unit, and the critical stability section discrimination unit have been described in detail in the above-mentioned nonlinear finite element discrimination method for the critical stability section of an underground cavern, and will not be repeated here in this embodiment.

[0075] Based on the same inventive concept, embodiments of the present invention also provide an electronic device. Figure 3 This is a structural block diagram of an electronic device provided in an embodiment of the present invention. Figure 3 As shown, an embodiment of the present invention provides an electronic device including: one or more processors 101, a memory 102, and one or more I / O interfaces 103. The memory 102 stores one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement any of the discrimination methods described in the above embodiments; the one or more I / O interfaces 103 are connected between the processor and the memory, configured to enable information interaction between the processor and the memory.

[0076] The processor 101 is a device with data processing capabilities, including but not limited to a central processing unit (CPU); the memory 102 is a device with data storage capabilities, including but not limited to random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), and flash memory (FLASH); the I / O interface (read / write interface) 103 is connected between the processor 101 and the memory 102, and can realize information interaction between the processor 101 and the memory 102, including but not limited to a data bus (Bus).

[0077] In some embodiments, the processor 101, memory 102, and I / O interface 103 are interconnected via bus 104, and thus connected to other components of the computing device.

[0078] In some embodiments, the one or more processors 101 include a field-programmable gate array.

[0079] This invention also provides a computer-readable medium. The computer-readable medium stores a computer program, which, when executed by a processor, implements the steps in any of the discrimination methods described in the above embodiments. The computer-readable storage medium may be volatile or non-volatile.

[0080] This invention also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code. When the computer-readable code is run in the processor of an electronic device, the processor in the electronic device executes the above-described discrimination method.

[0081] Those skilled in the art will understand that all or some of the steps, systems, and apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software can be distributed on a computer-readable storage medium, which may include computer storage media (or non-transitory media) and communication media (or transient media).

[0082] As is known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information, such as computer-readable program instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), static random access memory (SRAM), flash memory or other memory technologies, portable compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, it is known to those skilled in the art that communication media typically contain computer-readable program instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0083] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0084] The computer program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing state information from the computer-readable program instructions. This electronic circuitry can execute the computer-readable program instructions to implement various aspects of the invention.

[0085] The computer program product described herein can be implemented specifically through hardware, software, or a combination thereof. In one alternative embodiment, the computer program product is specifically embodied in a computer storage medium; in another alternative embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0086] Various aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0087] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0088] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0089] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0090] Example embodiments have been disclosed herein, and while specific terminology has been used, it is for illustrative purposes only and should be construed as such, and is not intended to be limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of the invention as set forth in the appended claims.

Claims

1. A nonlinear finite element method for determining the critical stability section of an underground cavern, characterized in that, include: Determine the rock mass strain softening parameters based on rock mechanics tests in actual engineering projects; The constitutive model of the rock mass is further developed based on the aforementioned rock mass strain softening parameters; Based on the constitutive model of the rock mass after secondary development, a nonlinear finite element initial model is constructed to solve the critical stability section of the underground cavern. Based on the constitutive model of the rock mass after secondary development, a nonlinear finite element initial calculation model for the critical stability section of underground caverns is constructed. The specific methods include: Based on the actual excavation conditions of the underground cavern, a finite element model of the underground engineering was constructed, including the cavern geometry, excavation steps, and initial geostress field. The model was meshed using transition mesh technology, and corresponding parameters and boundary conditions were set. The initial nonlinear finite element model is solved to obtain the overall tangent stiffness of the model at each calculation step. The nonlinear finite element model is then solved to obtain the overall tangent stiffness at each calculation step. Specifically, this involves: directly obtaining the overall tangent stiffness matrix using a nonlinear finite element solver; when the nonlinear finite element solver cannot directly obtain the overall tangent stiffness matrix, automatically extracting the overall tangent stiffness matrix under the current state using a developed script; real-time monitoring of the plastic zone area or feature point displacement of the model; and extracting the tangent stiffness matrix for each subsequent calculation step when the plastic zone area or displacement exceeds a preset threshold. Based on the overall tangent stiffness, the minimum eigenvalue of the overall tangent stiffness matrix is ​​calculated; the specific method for calculating the minimum eigenvalue of the overall tangent stiffness matrix based on the overall tangent stiffness includes: calling the eigenvalue calculation solver to solve for the eigenvalues ​​of the overall tangent stiffness matrix at each iteration step, and sorting all the eigenvalues ​​from smallest to largest to obtain the minimum eigenvalue; Based on the minimum eigenvalue, the critical stability section of the underground cavern is determined.

2. The method according to claim 1, characterized in that, The rock mass strain softening parameters are the rock mass parameters when the strength gradually decreases as the strain increases after the rock mass material reaches its peak strength, including at least the softening modulus and residual strength.

3. The method according to claim 1, characterized in that, Based on rock mechanics tests in actual engineering projects, the rock mass strain softening parameters are determined. The specific methods include: obtaining the stress-plastic strain curve in the actual engineering project based on the rock mechanics tests, and performing linear, exponential, or piecewise softening fitting on the stress-plastic strain curve to obtain the rock mass strain softening parameter function.

4. The method according to claim 1, characterized in that, The rock mass constitutive model is further developed based on the rock mass strain softening parameters. The specific method includes: using the rock mass constitutive model that comes with the user material subroutine module in the finite element solver, the constitutive model is further developed, and the rock mass strain softening parameters are imported into the constitutive model to obtain a rock mass constitutive model that conforms to the actual engineering situation.

5. The method according to claim 1, characterized in that, Based on the aforementioned minimum eigenvalue, the critical stability section of underground caverns is determined. Specific methods include: The minimum eigenvalue is compared with the value 0. When the minimum eigenvalue is greater than or equal to 0, the cavern at that time step is in a stable state. The minimum eigenvalue at the next time step is calculated. If the minimum eigenvalue after traversing the overall tangent stiffness matrix of all calculation time steps is greater than or equal to 0, it indicates that the initial cavern shape is in a self-stable state. At this time, the initial nonlinear finite element calculation model of the critical stability section of the underground cavern needs to be adjusted, and the above steps are repeated until the minimum eigenvalue is less than 0. When the minimum eigenvalue is less than 0, the cavern at that time step is unstable, and the corresponding cavern section state is marked as the critical section state, generating an underground cavern early warning signal.

6. A nonlinear finite element discrimination system for the critical stability section of an underground cavern, characterized in that, include: The system comprises the following units: rock mass strain softening parameter determination unit, rock mass constitutive model secondary development unit, underground cavern critical stability section construction unit, overall tangential stiffness acquisition unit, minimum eigenvalue calculation unit, and critical stability section discrimination unit; among which: The rock mass strain softening parameter determination unit is used to determine the rock mass strain softening parameters based on rock mechanics tests in actual engineering projects. The rock mass constitutive model secondary development unit is used to perform secondary development of the rock mass constitutive model based on the rock mass strain softening parameters; This is used to construct a nonlinear finite element initial model for solving the critical stability section of underground caverns based on the constitutive model of the rock mass after secondary development. The overall tangent stiffness acquisition unit is used to solve the nonlinear finite element model and obtain the overall tangent stiffness of the model at the corresponding calculation time step. The minimum eigenvalue calculation unit is used to calculate the minimum eigenvalue of the overall tangent stiffness matrix based on the overall tangent stiffness. The critical stability section discrimination unit is used to discriminate the critical stability section of the underground cavern based on the minimum characteristic value.

7. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the discrimination method as described in any one of claims 1 to 5.

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