A method, medium, and product for determining the optimal stable cross-section of a large-span, flat-shaped cavern.

Abstract

This invention discloses a method for determining the optimal stable cross-section of a large-span, flat cavern, relating to the fields of geotechnical engineering and underground structure design. The method first establishes a parametric geomechanical model using the cavern span L, crown rise S, and sidewall height H as control parameters. Second, based on the mechanical properties of the surrounding rock, a critical stability criterion is defined, with the comparison of circumferential strain and ultimate strain as its core. Then, using a particle swarm optimization algorithm, under preset geometric constraints and with the critical stability criterion as boundary conditions, a multi-objective iterative optimization calculation is performed on the parameter set (L, S, H). Finally, the target parameter set (Lf, Sf, Hf) that satisfies the critical stability state and has optimal geometric dimensions is output as the optimal stable cross-section solution. This invention automates and optimizes cross-section design, enabling the search for the most economical and efficient cavern cross-section shape while ensuring the self-stability of the surrounding rock, effectively overcoming the shortcomings of traditional design methods that rely on experience and are difficult to optimize.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering and underground structure design technology, specifically to a method, medium, and product for determining the optimal stable cross-section of a large-span flat cavern. Background Technology

[0002] Existing methods for determining critical stability sections primarily focus on highway and railway tunnels, mainly circular or horseshoe-shaped tunnels. Circular tunnels are influenced by a single factor (tunnel radius), while multi-centered horseshoe-shaped tunnels are often studied using proportional scaling, and their essential influencing factor is also singular. Furthermore, existing numerical simulation methods mainly rely on overall strength reduction, evaluating stability based on safety factors or plastic zone continuity, failing to achieve the optimal stable shape under specific geological conditions. Moreover, the calculations all employ conventional single-objective iterative calculations, unable to achieve rapid and efficient optimization calculations for multi-objective problems.

[0003] For large-span, flat-shaped tunnels, the geometric influencing factors are not unique, and the control parameters of their stable cross-sections are simultaneously affected by the span, rise, and wall height. Their stress patterns also differ from circular or horseshoe-shaped tunnels, with the span often becoming the dominant factor, requiring greater attention to crown deformation. Therefore, finding a multi-objective-based global optimization algorithm to determine the limiting cross-section of large-span, flat-shaped tunnels represents a significant innovation in both methodology and technology. Summary of the Invention

[0004] In view of the technical defects and drawbacks existing in the prior art, embodiments of the present invention provide a method, medium, and product for determining the optimal stable cross-section of a large-span flat cavern to overcome or at least partially solve the above problems. The specific solutions are as follows:

[0005] As a first aspect of the present invention, a method for determining the optimal stable cross-section of a large-span flat-type cavern is provided, comprising the following steps:

[0006] S1. A parameterized geomechanical model of the cavern cross section is established using the cavern span L, the arch rise S, and the sidewall height H as geometric control parameters.

[0007] S2, Based on the mechanical properties of the surrounding rock, a critical stability criterion based on the mechanical parameters of the surrounding rock is defined to quantitatively determine the stability of the cavern;

[0008] S3, using the particle swarm optimization algorithm, under preset geometric constraints, and with the stability critical criterion as the boundary condition, perform multi-objective iterative optimization calculation on the parameter set (L,S,H);

[0009] S4, outputs the objective parameter set (L) that satisfies the critical stability state and has optimal geometry. f ,S fH f ), which serves as the optimal stable cross-sectional solution for the large-span flat-type cavern.

[0010] Compared to existing technologies that rely on engineers' experience, perform numerous repetitive calculations, or use simplified formulas, this invention combines parametric modeling, explicit stability criteria, and intelligent optimization algorithms (PSO) to automatically search for and output the cross-sectional solution with optimal geometry under critical stability conditions. This greatly improves design efficiency, ensures the scientific validity and optimality of the results, and reduces reliance on human experience.

[0011] Further, step S1 includes:

[0012] A rectangular coordinate system is established with the vertical line at the midpoint of the cavern span as the vertical axis and the horizontal line at the top of the side wall as the horizontal axis;

[0013] The arch of the cavern is formed by a circular arc, the center point D of which lies in the rectangular coordinate system, and its radius R is determined by the span L and the sag S using the formula... Uniquely certain;

[0014] Based on Saint-Venant's principle, the dimensions of the model's side boundary are set to 2 to 3 times the cavern span L or the total height (S+H);

[0015] Based on the input parameter set (L,S,H), the corresponding geomechanical model is generated using finite element method or discrete element method numerical analysis software.

[0016] This invention enables rapid, accurate, and parametric generation of cavern cross-sections, particularly the arch shape. By defining the cross-section using a rigorous geometric coordinate system and mathematical formulas (such as the formula for determining the radius R of the arc), the accuracy and consistency of each modeling step are ensured. Compared to existing technologies that may employ approximate shapes or manual modeling, this method can be seamlessly integrated with numerical analysis software to achieve automated model generation, laying the foundation for subsequent batch automated calculations and optimizations.

[0017] Furthermore, the stability critical criterion specifically includes:

[0018] Ultimate strain calculation: based on the uniaxial compressive strength σ of the rock mass cm and rock mass elastic modulus E m Through the formula ε cr =σ cm / E m Calculate the ultimate strain ε cr ;

[0019] Circumferential strain derivation: Based on the arch crown settlement ΔS, the circumferential strain ε around the tunnel is calculated using geometric deformation relationships. The specific formula set is as follows:

[0020] Arch radius before settlement: ;

[0021] Arch radius after settlement: ;

[0022] Arch length before settlement: ;

[0023] Arch length after settlement: ;

[0024] Circumferential strain: ;

[0025] The calculated ε is compared with the ultimate strain ε cr By comparing the results, it can be determined whether the cavern is in a critical stable state.

[0026] This invention proposes an innovative stability criterion based on the deformation capacity of rock mass rather than just its strength—the comparison between circumferential strain and ultimate strain. Traditional criteria are mostly based on the ratio of stress to strength (safety factor), while this invention introduces the concept of "ultimate strain" and derives a specific calculation formula for circumferential strain. This can more sensitively and directly reflect the deformation and failure mechanism of the surrounding rock, and is especially suitable for large-span flat caverns with high requirements for deformation control, making the judgment more precise and scientific.

[0027] Furthermore, the crown settlement ΔS is obtained through an automated numerical simulation process, specifically including:

[0028] Call numerical analysis software (such as FLAC / Ansys / UDEC) to automatically generate a geomechanical model and perform mechanical calculations based on the input parameter set (L, S, H);

[0029] The crown settlement ΔS is extracted from the calculation results as the core output variable.

[0030] Substituting ΔS into the set of geometric analytical formulas, we obtain... ,based on get:

[0031] ;

[0032] Real-time comparison of circumferential strain ε and ultimate strain ε of the test chamber cr If |ε / ε cr- If 1|≤0.01, it is marked as a critical stable state, and the corresponding parameter set (L,S,H) and its corresponding stability state are stored as the fitness evaluation basis of the particle swarm algorithm.

[0033] This invention achieves full-process automation and real-time integration. It links numerical simulation (obtaining ΔS), theoretical calculation (deriving ε), and stability determination (comparing with εcr) into an automated closed-loop process. Compared to the inefficient process of manual data extraction, calculation, and judgment in traditional methods, this scheme can be directly invoked by optimization algorithms, enabling unattended, rapid, and large-scale evaluation, which is key to ensuring the efficient execution of particle swarm optimization algorithms.

[0034] Furthermore, the iterative optimization calculation specifically includes:

[0035] Define the population size N, the maximum number of iterations G, the inertia weight ω, and the learning factor. and ;

[0036] Randomly initialize the positions of N particles and speed The position of each particle represents a set of parameters (L, S, H), for example, let be... = Its initial values ​​satisfy predefined geometric constraints;

[0037] For each particle, an automated numerical simulation process is invoked to obtain its corresponding circumferential strain ε around the hole.

[0038] Update the individual's optimal position based on the particle fitness evaluation rule. and the global optimal position ;

[0039] Based on individual optimal position and the global optimal position The particle velocity and position are updated according to the following formula:

[0040] ;

[0041] ;

[0042] Where r1 and r2 are uniformly random numbers. This records the position of the i-th particle with the best fitness in the iterations up to step k. This represents the position of the particle with the best fitness in the entire particle swarm during the iterations up to step k. Let be the position of the i-th particle in the k-th iteration step, and let represent a set of cavern geometric parameters, denoted as . = , Let be the velocity vector of the i-th particle in the k-th iteration step;

[0043] When the maximum number of iterations G is reached or the convergence condition is met (e.g., satisfying the condition), If the parameter remains unchanged for three consecutive iterations, then stop the iteration and output the parameter set (L) corresponding to the global optimal position. f ,S f H f () is the optimal solution.

[0044] This invention introduces the Particle Swarm Optimization (PSO) algorithm to solve multi-objective optimization problems. The PSO algorithm has the advantages of strong global search capability and fast convergence speed, making it very suitable for optimization in the high-dimensional, nonlinear parameter space (L, S, H) defined in this invention. Compared with exhaustive search or traditional gradient descent, PSO can find the global or near-global optimal solution with fewer computations and in a shorter time, significantly improving optimization efficiency. The explicit convergence condition also ensures the termination of the algorithm and the output of the results.

[0045] Furthermore, the geometric constraints include:

[0046] The range of the cavern span L: 15m ≤ L ≤ 50m;

[0047] The range of the sag-to-span ratio S / L is: 0.1 ≤ S / L ≤ 0.3;

[0048] The range of the span ratio H / L is: 0.1 ≤ H / L ≤ 0.5.

[0049] This invention provides a reasonable and practical search space (geometric constraints) for optimization problems. These constraints (such as the span-to-span ratio of 0.1-0.3) are based on common sense and standards in engineering, ensuring that the optimization algorithm searches only within the range of parameters that are practically meaningful. This avoids a large number of invalid calculations and greatly improves the efficiency of the optimization process and the feasibility of the results.

[0050] Furthermore, N∈[20,50], ω∈[0.4,0.9], = =1.49445, r1, r2 are uniformly distributed random numbers in the range [0,1] (generated independently in each step).

[0051] This invention optimizes the hyperparameter settings of the PSO algorithm. The given parameter range (e.g., N∈[20,50], ω∈[0.4,0.9]) is a commonly used effective interval verified in practice. Setting the learning factors c1 and c2 to a classic value (1.49445) helps to balance the algorithm's exploration and development capabilities, thereby ensuring that the optimization process can converge quickly while avoiding getting trapped in local optima, thus improving the reliability and stability of the algorithm.

[0052] In some embodiments, the particle fitness evaluation rule is executed according to the following priority rule:

[0053] Prioritize selecting the parameter set that brings the cavern to a critically stable state, i.e., satisfying |ε / ε cr- 1 | ≤ 0.01;

[0054] Among particles that do not meet the critical state, priority should be given to selecting Particles with smaller values;

[0055] For particles that satisfy the critical stable state, they are further sorted according to the following priority:

[0056] The one with the largest span L is optimal;

[0057] When L is the same, the one with the smallest sag S is the optimal one;

[0058] When L and S are the same, the side wall with the smallest height H is the optimal choice.

[0059] The optimal position of an individual and the global optimal position are obtained based on the particle fitness evaluation rules.

[0060] In practical applications, the particle fitness evaluation rule is used as the objective function, and the corresponding individual optimal position and global optimal position are found based on the rules in the objective function.

[0061] As a second aspect of the invention, a computer-readable storage medium is also provided, wherein a computer program is stored therein, and when executed by a computer, the computer program causes the computer to perform the steps in any of the above-described methods for determining the optimal stable cross-section of a large-span flat-type cavern. The computer-readable storage medium may be volatile or non-volatile.

[0062] As a third aspect of the present invention, a computer program product is also provided, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device executes any of the above-described methods for determining the optimal stable cross-section of a large-span flat-type cavern.

[0063] The present invention has the following beneficial effects:

[0064] This invention provides a method for determining the optimal stable cross-section of a large-span flat cavern based on particle swarm optimization (PSO). By limiting the height-to-span ratio (H / L) and the rise-to-span ratio (S / L) of the large-span flat cavern model to the characteristic parameters of span L, sidewall height H, and arch sag S, the method ensures the cavern shape is flat. For a specific lithological stratum, there must exist an optimal (L, S, H) parameter combination that satisfies the constraints of maximizing the span and minimizing the rise and sidewall height, serving as the ultimate stability cross-section of the cavern under those strata. Beyond this constraint, the cavern requires additional support measures to meet stability requirements; conversely, below this constraint, the cavern can achieve self-stability. Based on PSO, the method enables rapid searching of the globally optimal (L, S, H) parameter combination and establishes a corresponding analysis system, achieving parameterized automatic modeling calculation and rapid determination of the optimal stable cross-section parameters. Attached Figure Description

[0065] Figure 1 A flowchart illustrating a method for determining the optimal stable cross-section of a large-span flat-type cavern, as provided in an embodiment of the present invention;

[0066] Figure 2 This is a schematic diagram of the cross-sectional geometry of a flat, ultra-large span cavern provided in an embodiment of the present invention;

[0067] Figure 3 This is a schematic diagram of the ultimate strain calculation for a flat-shaped cavity provided in an embodiment of the present invention;

[0068] Figure 4 This invention provides a system architecture for determining the optimal cross-section of a large-span flat-type cavern under limit equilibrium conditions. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] 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.

[0071] Where there is no conflict, the various embodiments of the present invention and the features thereof may be combined with each other.

[0072] As used herein, the term “and / or” includes any and all combinations of one or more related enumerated entries.

[0073] 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.

[0074] 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.

[0075] In the technical solution of this invention, the collection, storage, use, processing, transmission, provision, and disclosure of user personal information all comply with relevant laws and regulations and do not violate public order and good morals. The use of user data in this technical solution follows relevant national laws and regulations (e.g., the "Information Security Technology - Personal Information Security Specification"). For example: appropriate measures are taken for personal information access control; restrictions are imposed on the display of personal information; the purpose of using personal information does not exceed the scope of direct or reasonable association; and explicit identity targeting is eliminated when using personal information to avoid precisely locating a specific individual.

[0076] To obtain the optimal cross-section of a large-span flat cavern under the limit equilibrium state under certain geological conditions, and thus provide an effective method for the design of ultra-large-span caverns in deep underground spaces, this invention proposes a method for determining the optimal stable cross-section of a large-span flat cavern based on particle swarm optimization algorithm. Figure 1 This is a flowchart illustrating a method for determining the optimal stable cross-section of a large-span flat-type cavern, as provided in an embodiment of the present invention.

[0077] Includes the following steps:

[0078] S1. Establish a parameterized geomechanical model: Using the cavern span L, the arch rise S, and the sidewall height H as geometric control parameters, establish a parameterized cavern cross-section geomechanical model.

[0079] S2, Define the stability criteria and critical conditions of the cavern: Based on the mechanical properties of the surrounding rock, define the critical stability criteria based on the mechanical parameters of the surrounding rock, which are used to quantitatively determine the stability of the cavern;

[0080] S3, Multi-objective optimization selection based on particle swarm optimization algorithm: Under the preset geometric constraints, the parameter set (L,S,H) is subjected to multi-objective iterative optimization calculation using the stability critical criterion as the boundary condition through particle swarm optimization algorithm;

[0081] S4, Determination of optimal parameters: Output the target parameter set (L) that satisfies the critical stability state and has optimal geometry. f ,S f H f ), which serves as the optimal stable cross-sectional solution for the large-span flat-type cavern.

[0082] In some embodiments, establishing a parametric geomechanical model includes:

[0083] Taking the following flat-shaped cavern as the research object, a typical cross-sectional shape is established, such as... Figure 2 Where L is the span of the flat cavern (unit: m), S is the rise of the cavern vault, H is the height of the cavern sidewalls, and D is the center point of the arched arc. The parametric features are:

[0084] A rectangular coordinate system is established with the midpoint of the cavern span as the vertical line and the top of the wall height as the horizontal line. It can be seen that, given the span L, sag S, and wall height H, a unique geometric model of the cavern can be established. Assuming the surrounding soil and rock are homogeneous, a parametric model based on the variation of (L, S, H) can be established using finite element or discrete element analysis software (such as FLAC, Ansys, UDEC, etc.). The side boundary dimensions of the model can be taken as 2 to 3 times the cavern span or height according to Saint-Venant's principle, establishing a mechanical model that satisfies the cavern boundary dimensions.

[0085] In some embodiments, defining cavern stability criteria and critical conditions includes:

[0086] Typically, the stability of a cavern can be assessed using a safety factor. A safety factor of 1 indicates a critical state. The safety factor can be calculated based on the strength reduction method, or by analyzing whether stress and displacement exceed allowable values, or whether plastic zone penetration has occurred. In numerical simulations, a specific criterion can be selected to determine whether a critical state has been reached, taking into account the specific application scenario and regulatory requirements.

[0087] Currently, there are no clear regulations for deformation control of ultra-large span flat caverns (span greater than 50m). Considering that ultra-large span caverns are mainly used in hydropower, special laboratories, and other fields, deformation control standards are often used as stability criteria. Furthermore, the allowable deformation value of large span caverns is related to the cavern geometry and the strength characteristics of the surrounding rock. This invention mainly elucidates the establishment of the optimal stable cavern shape for large span caverns under specific geological conditions. Therefore, under the assumption of isotropic strata, a limit strain control criterion corresponding to the geometric dimensions is proposed. In subsequent practical projects, appropriate stability criteria can be established based on actual strata conditions and parameters, without affecting the main idea of ​​this invention.

[0088] ①Limit strain criterion

[0089] After the stress redistribution of the surrounding rock in an ideal, ultra-large span, flat tunnel, the tangential rock mass around the tunnel is mainly under compression due to the arch shape. Therefore, the uniaxial compressive strength of the rock mass around the tunnel should be considered. When the tangential stress exceeds the uniaxial compressive strength, the rock mass is considered to have failed. Thus, the ultimate strain ε of the rock mass can be used. cr As an indicator for quantifying the degree of surrounding rock compression, that is, under bare tunnel conditions, when the surrounding rock of the tunnel should be less than the ultimate strain ε cr When the time limit is reached, the cavern can remain stable; when the time limit is exceeded, the surrounding rock of the cavern becomes unstable.

[0090] The ultimate strain of rock mass can be calculated using the following formula:

[0091]

[0092] Where, ε cr For the ultimate strain of the rock mass, σ cm E represents the uniaxial compressive strength of the rock mass (unit: MPa). m Rock mass elastic modulus (unit: GPa);

[0093] The above-mentioned ultimate strain is applicable to isotropic homogeneous rock strata. Depending on the actual situation, empirical formulas under different lithological conditions can be selected to solve for the ultimate strain value.

[0094] ② Limit strain calculation in the model

[0095] Based on the stability criterion of ultimate strain, the ultimate strain around the tunnel can be calculated according to the settlement change of the arch of the flat-type ultra-large span tunnel. The specific calculation is as follows: Figure 3 .

[0096] BB The settlement of the arch after the excavation of the cavern is shown at point D, which is the arc. The center of the circle, AD is radius; D For arc Center, AD for radius.

[0097] Remembering BB for AD is the radius R, AD For R (Unit: m), then we have:

[0098]

[0099]

[0100] By solving, we can obtain:

[0101]

[0102]

[0103] Similarly, it can be calculated:

[0104]

[0105] The circumferential strain around the tunnel caused by tunnel settlement can be obtained as follows:

[0106]

[0107] Therefore, the stability critical condition based on the limit strain criterion can be obtained as follows:

[0108]

[0109] When the circumferential strain around the tunnel is caused by the settlement of the arch... greater than the ultimate strain At that time, it was believed that the cavern had been damaged.

[0110] In some embodiments, the geomechanical model and stability criteria can be implemented by establishing an automated numerical simulation process, including:

[0111] As can be seen from the aforementioned step S1, finite element or discrete element analysis software (such as FLAC, Ansys, UDEC, etc.) can be used to establish a command flow driven mechanical model based on the freely varying parameter set of span L, rise S and wall height H. Based on the criterion of ultimate strain, the settlement of the arch is recorded, the model tunnel type is analyzed for instability of each parameter set, the parameter set is saved and recorded, and the parameters are continuously automatically adjusted until the parameter set that meets the optimal conditions is found.

[0112] In some embodiments, multi-objective optimization selection based on particle swarm optimization includes:

[0113] In the automated numerical simulation process, if no restrictions are imposed on the parameter set (L, S, H), there will be an infinite number of parameter sets, which may not necessarily meet the requirements for a flat cavity shape. Therefore, a particle swarm optimization algorithm can be used to find the optimal cavity shape parameters that meet the requirements, combining the objective function and constraints, as follows:

[0114] 1) Constraints

[0115] ① Critical state constraints: can be expressed as: This indicates that the state is relatively close to the critical state.

[0116] ② Geometric Constraints: To ensure that the searched parameter set satisfies the flat-type cavern requirement, and that the span is within a reasonable range, the geometric constraints are determined as follows (assuming the geological conditions are Class I surrounding rock):

[0117] a. The span is limited to: 15m ≤ L ≤ 50m

[0118] b. The S / L ratio ranges from (0.1 to 0.3).

[0119] c. The H / L ratio ranges from (0.1 to 0.5).

[0120] 2) Objective function

[0121] The objective function is used to evaluate the quality of individual particles. In this case, the optimal position of the individual and the global optimal position are updated according to the comparison rule (i.e., the particle fitness evaluation rule).

[0122] In the optimal cavity shape particle search process for a flat, large-span cavity, priority is given to ensuring that the parameter set meets the critical stability state. Among the particles that do not meet the critical state, priority is given to selecting... Particles with smaller values.

[0123] Secondly, the largest span is optimal, then the smallest sag is optimal, and finally the smallest sidewall height is optimal. Since the particle swarm algorithm is usually applicable to a single particle, it can traverse all particles and use the above rules to find the optimal particle as the global leader, that is, the global optimal position.

[0124] 3) Algorithm Flow

[0125] ① Initialize the particle swarm. The initial population size is N (generally 20-50 groups). Randomly determine N groups of parameters that satisfy the geometric constraints as the swarm particles. Set the initial velocity to 0. Initialize the optimal position of each individual particle as its current position. Give the number of iteration steps G (determined according to the convergence situation).

[0126] ② Initialize the global optimal position: According to the comparison rules in the objective function, traverse all particles in the initial population and select the particle that satisfies the above rules as the initial global optimal position particle.

[0127] ③ Update speed and location:

[0128] Based on the comparison rules in the objective function, the individual extreme values ​​of the same particle are continuously sought during the iterative process. and the population extrema of all particles in the population. The particle's velocity and position information are updated using the following formula:

[0129]

[0130]

[0131] The above formula is the particle swarm optimization algorithm formula: k is the number of iterations; Let be the particle velocity at the k-th iteration step, representing the direction and magnitude of the particle's motion; This represents the position of the particle in the k-th iteration step, i.e., the value of the optimized variable; The inertia weight (can be a fixed value such as 0.9, or decrease linearly with the number of iterations); , As a learning factor, it can be taken = =1.49445, , is a random number uniformly distributed in the range [0, 1].

[0132] ④Result Output

[0133] After multiple iterative calculations, the variable values ​​(L) that satisfy the objective function are finally found. f S f H f ), which serves as the optimal stable cross-sectional parameter for large-span flat-type caverns.

[0134] In some embodiments, determining the optimal parameters includes:

[0135] Based on the above iterative calculations, the final value of the objective function variable (L) f S f H f The optimal stable cross-sectional parameters for large-span flat-type tunnels are denoted as .

[0136] Based on the above modeling and optimization algorithm process and ideas, an automatic optimization parametric modeling → calculation → optimization algorithm → result output system can be built to find the optimal stable cross-sectional parameters of the optimal large-span flat cavern.

[0137] Ultimately, based on the above methods, it can be implemented through an integrated system, see [link to relevant documentation]. Figure 4 It can contain the following modules:

[0138] (1) Geological database module: stores geological exploration data of the project area;

[0139] (2) Parametric modeling module: Automatically generates numerical models based on geometric parameters;

[0140] (3) Optimization algorithm engine: Implements the priority particle swarm optimization algorithm;

[0141] (4) Parallel computing cluster: Distributed processing of numerical simulation calculations;

[0142] (5) Numerical simulation core: Perform stress balance simulation analysis of tunnel excavation under different tunnel type parameter groups;

[0143] (6) Results Analysis Module: Extract key mechanical indicators and safety factors;

[0144] (7) Visual interface: Two-dimensional / three-dimensional display of the optimization process and the final cross section.

[0145] Finally, it can be applied to specific engineering projects: Based on the application scenario and geological conditions, combined with relevant specifications, the span range of the self-stabilizing cavern can be roughly determined. Then, based on the shape of the target cavern, the sag-to-height ratio and height-to-span ratio of the flat cavern can be determined, thereby narrowing down the calculation range. Then, the optimal cross-section under the limit equilibrium state of the large-span flat cavern can be determined through calculation. Using this cross-section as a reference type, the target cavern can be expanded by combining multiple reference cross-sections, and the support design scheme can be determined, thus completing the design of the ultra-large span cavern.

[0146] This invention also provides a computer-readable storage medium storing a computer program. When executed by a computer, the computer program causes the computer to perform the steps in any of the methods for determining the optimal stable cross-section of a large-span flat-type cavern as described in the above embodiments. The computer-readable storage medium can be volatile or non-volatile.

[0147] 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 method for determining the optimal stable cross-section of a large-span flat-type tunnel.

[0148] 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).

[0149] 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.

[0150] 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.

[0151] 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.

[0152] 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.

[0153] 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.

[0154] 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.

[0155] 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.

[0156] 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.

[0157] 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.

[0158] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the optimal stable cross-section of a large-span, flat-shaped cavern, characterized in that, Includes the following steps: S1. A parameterized geomechanical model of the cavern cross section is established using the cavern span L, the arch rise S, and the sidewall height H as geometric control parameters. S2, Based on the mechanical properties of the surrounding rock, a critical stability criterion based on the mechanical parameters of the surrounding rock is defined to quantitatively determine the stability of the cavern; The stability critical criterion specifically includes: Ultimate strain calculation: based on the uniaxial compressive strength σ of the rock mass cm and rock mass elastic modulus E m Through the formula ε cr =σ cm / E m Calculate the ultimate strain ε cr ; Circumferential strain derivation: Based on the arch crown settlement ΔS, the circumferential strain ε around the tunnel is calculated using geometric deformation relationships. The specific formula set is as follows: Arch radius before settlement: ; Arch radius after settlement: ; Arch length before settlement: ; Arch length after settlement: ; Circumferential strain: ; The calculated ε is compared with the ultimate strain ε cr By comparing the results, it can be determined whether the cavern is in a critical stable state; S3, using a particle swarm optimization algorithm, under preset geometric constraints and with the stability critical criterion as boundary conditions, performs multi-objective iterative optimization calculations on the parameter set (L,S,H); the iterative optimization calculations specifically include: Define the population size N, the maximum number of iterations G, the inertia weight ω, and the learning factor. and Generate uniformly distributed random numbers r1 and r2; Randomly generate the initial positions of N particles. and speed Each particle's position represents a set of parameters (L, S, H), whose initial values ​​satisfy predefined geometric constraints. For each particle, an automated numerical simulation process is invoked to obtain its corresponding circumferential strain ε around the hole. Update the individual's optimal position based on the particle fitness evaluation rule. and the global optimal position ; Based on individual optimal position and the global optimal position The particle velocity and position are updated according to the following formula: ； ； in, This represents the position record of the i-th particle with the best fitness in the iterations up to step k. This represents the position of the particle with the best fitness in the entire particle swarm during the iterations up to step k. Let i be the position of the i-th particle in the k-th iteration step. Let be the velocity vector of the i-th particle in the k-th iteration step; The iteration stops when the maximum number of iterations G is reached or the convergence condition is met. The particle fitness evaluation rules are implemented according to the following priority rules: Prioritize selecting the parameter set that brings the cavern to a critically stable state, i.e., satisfying... ; Among particles that do not meet the critical state, priority should be given to selecting Particles with smaller values; For particles that satisfy the critical stable state, they are further sorted according to the following priority: The one with the largest span L is optimal; When L is the same, the one with the smallest sag S is the optimal one; When L and S are the same, the side wall with the smallest height H is the optimal choice. Based on the particle fitness evaluation rule, the optimal position of individuals and the global optimal position in the particle swarm optimization algorithm are obtained and updated. S4, outputs the objective parameter set (L) that satisfies the critical stability state and has optimal geometry. f ,S f H f ), which serves as the optimal stable cross-sectional solution for the large-span flat-type cavern.

2. The method for determining the optimal stable cross-section of a large-span flat-type cavern according to claim 1, characterized in that, Step S1 includes: A rectangular coordinate system is established with the vertical line at the midpoint of the cavern span as the vertical axis and the horizontal line at the top of the side wall as the horizontal axis; The arch of the cavern is formed by a circular arc, the center point D of which lies in the rectangular coordinate system, and its radius R is determined by the span L and the sag S using the formula... Uniquely certain; Based on the input parameter set (L,S,H), the corresponding geomechanical model is generated using finite element method or discrete element method numerical analysis software.

3. The method for determining the optimal stable cross-section of a large-span flat-type tunnel according to claim 1, characterized in that, The crown settlement ΔS was obtained through an automated numerical simulation process, specifically including: The numerical analysis software is invoked to automatically generate a geomechanical model and perform mechanical calculations based on the input parameter set (L, S, H). The crown settlement ΔS is extracted from the calculation results as the core output variable. Substitute ΔS into the set of geometric analytical formulas and calculate sequentially: ； ； Real-time comparison of circumferential strain ε and ultimate strain of the test chamber If satisfied This is then marked as a critical stable state, and the corresponding parameter set (L,S,H) and its corresponding stability state are stored as the basis for fitness evaluation in the particle swarm algorithm.

4. The method for determining the optimal stable cross-section of a large-span flat-type cavern according to claim 1, characterized in that, The geometric constraints include: The range of the cavern span L: 15m ≤ L ≤ 50m; The range of the sag-to-span ratio S / L is: 0.1 ≤ S / L ≤ 0.3; The range of the span ratio H / L is: 0.1 ≤ H / L ≤ 0.

5.

5. The method for determining the optimal stable cross-section of a large-span flat-type tunnel according to claim 1, characterized in that, N∈[20,50], ω∈[0.4,0.9], r1 and r2 are uniformly distributed random numbers in the range [0,1].

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a computer, causes the computer to perform the steps in the method for determining the optimal stable cross-section of a large-span flat-type cavern as described in any one of claims 1-5.

7. A computer program product, characterized in that, Includes computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device executes the method for determining the optimal stable cross-section of a large-span flat-type cavern as described in any one of claims 1-5.

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