Roadway anchor rod group support parameter intelligent optimization method based on unbalanced force

Abstract

The invention relates to the technical field of mining engineering and geotechnical engineering support design, and discloses a roadway anchor rod group support parameter intelligent optimization method based on unbalanced force, and the method comprises the steps: building a surrounding rock finite element model, calculating a plastic stress increment through employing a minimum plastic complementary energy principle, and mapping the plastic stress increment into a node unbalanced force vector; an unbalanced force field reflecting reinforcement requirements is constructed, and an initial scheme is generated according to the unbalanced force field. Then, a virtual anchor rod unit is introduced to establish a nonlinear coupling model, an incremental balance equation is solved, and whether the unbalanced force is smaller than a threshold value or not is judged; if so, outputting an optimal parameter; otherwise, a comprehensive objective function containing safety and economy is constructed, new parameters are obtained through searching and decoding by means of the particle swarm algorithm, and the virtual anchor rod unit is re-entered for calculation to form a closed loop until convergence is achieved. According to the method, intelligent optimization is driven through a physical mechanism, the problem that a traditional design lacks a mechanical basis is solved, and accurate optimization of support parameters is achieved.

Description

Technical Field

[0001] This invention relates to the field of support design technology in mining engineering and geotechnical engineering, specifically to an intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces. Background Technology

[0002] After the excavation of deep mine roadways, the redistribution of stress in the surrounding rock can lead to large deformations or even failure. Active support using bolt groups is the primary means of controlling surrounding rock stability. In existing support design systems, engineering analogy and traditional numerical simulation-based auxiliary design are the mainstream approaches. Engineers typically perform qualitative analysis based on stress contour maps, displacement contour maps, or the distribution range of the plastic zone output from numerical calculations, estimating the length, spacing, and installation angle of the bolts based on engineering experience. This design model lacks clear quantitative mechanical indicators, failing to accurately quantify the self-supporting capacity gap of the surrounding rock at specific locations and the required external compensation force. This often results in significant arbitrariness in the selection of support parameters, easily leading to safety hazards due to insufficient support strength or resource waste due to excessive support.

[0003] Furthermore, in numerical analysis of anchor bolt support systems, accurately simulating the interaction mechanism between the anchor bolt and the surrounding rock is crucial for evaluating the support effect. Existing conventional analysis models often simplify the anchorage interface, such as assuming coordinated displacement (perfect bonding) between the anchor bolt and the surrounding rock nodes or using only simple linear spring elements to simulate the contact. However, in actual engineering, the anchorage interface exhibits nonlinear mechanical behavior, including bond slip, debonding softening, and friction effects. This simplification neglects the release effect of interface slip on the deformation of the surrounding rock, leading to deviations between the calculated deformation of the surrounding rock and the stress state of the anchor bolt and the actual situation, thus reducing the guiding value of the numerical simulation results for engineering design.

[0004] At the optimization level, the current process for determining support parameters mainly relies on manual trial and error, where designers manually adjust parameters, run models, and verify the results. Since tunnel support involves multiple parameters such as anchor length, spacing, preload, and angle, and these parameters have complex nonlinear coupling relationships, manual trial and error cannot cover all possible parameter combinations, making it impossible to find the true global optimum in the multi-dimensional parameter space. Furthermore, existing design processes typically focus on meeting single safety and stability requirements, lacking effective means to incorporate project cost as a core variable into the mathematical model for simultaneous optimization, making it difficult to achieve a precise balance between safety and economic indicators during the design phase. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces. This method solves the problems of lack of quantitative mechanical basis for parameter selection in existing roadway support designs, calculation deviations caused by simplification of anchor interface simulation, and the difficulty in achieving global synergistic optimization of safety and economy by relying on manual trial and error.

[0006] To achieve the above objectives, this invention provides an intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces, comprising the following steps: An initial finite element model of the surrounding rock is constructed. Geometric entities are established based on geological data and discretized into a mesh. In the stress concentration areas around the tunnel, eight-node hexahedral elements are used to divide the three-dimensional geometric entities, forming a mesh model composed of nodes and elements. The surrounding rock material parameters and yield criterion are defined. The stiffness matrix of each element is calculated based on the principle of virtual work, and the global stiffness matrix of the mechanical system to be analyzed is generated according to the node topological relationships. Displacement boundaries and initial geostress fields are then applied.

[0007] Unbalanced force field diagnosis is performed. The mechanical system under analysis is simulated during excavation and unloading. Based on the linear elastic assumption, the elastic test stress of each element is calculated. For the integration point determined to be yielding, the principle of minimum plastic residual energy is used to find the true stress tensor located on the yield surface, minimizing the plastic complementary residual energy increment between the true stress tensor and the elastic test stress. The difference between the elastic test stress and the true stress tensor is calculated to obtain the plastic stress difference tensor as the plastic stress increment. Based on the principle of virtual work, the integral of the plastic stress difference tensor within each element is transformed into an unbalanced force vector at each element node. The unbalanced force vectors at all element nodes are assembled and superimposed according to node number to construct an unbalanced force field, thereby quantitatively characterizing the size of the self-supporting capacity gap in the surrounding rock and the direction of the required external support force.

[0008] An initial plan is generated. The node distribution characteristics are extracted based on the unbalanced force field, and the regional reinforcement requirements are analyzed. The distribution of the unbalanced force vector along the radial direction of the nodes within the area to be supported is searched, and the unbalanced force modulus along the depth of the surrounding rock is recorded. The anchor bolt length is determined based on the minimum depth value where the unbalanced force modulus meets the attenuation coefficient requirement. The resultant force vector of the unbalanced force vectors of all nodes within the area to be supported and its projection onto the roadway surface in the normal direction are calculated to obtain the total required force for regional normal reinforcement. The total number of anchor bolts required is calculated based on the ratio of this required force to the ultimate bearing capacity of a single anchor bolt, and the anchor bolt spacing is derived by reverse calculation. The initial installation angle of the anchor bolts is determined based on the opposite direction of the local resultant force vector, thereby obtaining the initial support parameter set.

[0009] A coupled analysis model is established. A bond-slip constitutive relation describing the nonlinear shear behavior of the interface is introduced, employing a double-exponential bond-slip constitutive model that includes the bond strength function during the softening stage. The interface tangential stiffness is obtained by differentiating the relative slip of the interface in this model, and the contact stiffness matrix is ​​derived accordingly. The contact stiffness matrix is ​​superimposed on the global stiffness matrix to construct an incremental equilibrium equation system incorporating the cooperative deformation mechanism of the anchor bolt and the surrounding rock. Solving the equation system yields the support effect of this support scheme on the surrounding rock, and it is determined whether the unbalanced force of the surrounding rock is less than a given threshold. If the unbalanced force is less than the given threshold, the current support scheme is output as the optimal support parameters; otherwise, the following steps are executed.

[0010] A comprehensive objective function is constructed. The residual unbalanced force norm, characteristic point displacement, anchor bolt axial force, and material cost are selected as evaluation indicators. The normalized maximum displacement, normalized maximum unbalanced force, normalized anchor bolt axial force, and normalized material cost for each scheme are calculated. These four normalized indicators are combined through a weighted summation to form a comprehensive fitness function that quantitatively evaluates the safety, stability, and economy of the scheme.

[0011] Global optimization is performed. Support parameters are encoded, and the particle population is initialized using the initial support parameter set. Based on the incremental balance equations and the comprehensive fitness function, the particles are driven to iteratively search in multi-dimensional space. The specific strategy for constraining the variable range using boundary mechanisms is as follows: when the particle update position exceeds a preset range, a forced correction is performed; if the particle update position is less than the lower bound, it is set as the lower bound and the particle velocity is set to zero; if the particle update position is greater than the upper bound, it is set as the upper bound and the particle velocity is set to zero. The new support parameters are obtained, and the virtual anchor element is re-entered to calculate and solve for the unbalanced force until the unbalanced force is less than a given value, at which point the optimization stops, and the optimal particle is determined.

[0012] Output optimal parameters. Extract the position vector corresponding to the globally optimal particle, and decode it into specific parameters conforming to the engineering modulus through nearest neighbor mapping and directional rounding strategies. Verify the decoded specific parameters using the strength reduction method and calculate the system safety factor. After the system safety factor verification is passed, generate a report containing a 3D topology model and a bill of materials as the final solution output.

[0013] This invention provides an intelligent optimization method for roadway anchor group support parameters based on unbalanced forces. It has the following beneficial effects: 1. This invention solves for the plastic stress increment by using the principle of minimum plastic residual energy and maps it to a nodal unbalanced force vector, thus constructing an unbalanced force field that reflects local damage to the surrounding rock and the need for reinforcement. This technical solution can quantitatively characterize the size of the gap in the self-supporting capacity of the surrounding rock and the direction of the required external support force, thereby providing a direct quantitative mechanical basis for determining the length, spacing, and installation angle of anchor bolts. It solves the problems of traditional design methods relying on trial and error based on manual experience and lacking clear quantitative indicators.

[0014] 2. This invention introduces a double-exponential bond-slip constitutive model into finite element analysis, derives the contact stiffness matrix, and superimposes it onto the global stiffness matrix, establishing a coupled analysis model of anchor bolts and surrounding rock that considers the nonlinear shear behavior of the interface. This method can accurately describe the cooperative deformation mechanism and load transfer law between the anchor bolt and the surrounding rock, eliminating the calculation deviations caused by neglecting interface slip or simplifying the constitutive model in traditional methods, and improving the accuracy of stress analysis of the support structure.

[0015] 3. This invention constructs a comprehensive fitness function that includes residual unbalanced force, characteristic point displacement, anchor bolt axial force, and material cost, and uses a particle swarm optimization algorithm to perform global optimization. This scheme incorporates the safety and economic indicators of support design into a unified optimization framework, and can automatically search for the global optimal solution in a multidimensional parameter space that satisfies the incremental balance equation, achieving a reasonable trade-off between effectively controlling surrounding rock deformation and reducing overall engineering costs. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall process of the method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the finite element discretization model of the tunnel surrounding rock system of the present invention; Figure 3 This is a flowchart of the unbalanced force diagnosis based on the principle of minimum plastic residual energy of the present invention. Detailed Implementation

[0017] The technical solutions in 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 some embodiments of the present invention, and not all 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.

[0018] See attached document Figure 1 This invention provides an intelligent optimization method for roadway anchor group support parameters based on unbalanced forces. It combines physically driven numerical calculations with intelligent optimization algorithms to achieve quantification and optimization of roadway support design. The method includes the following steps: S10, construct the initial finite element numerical model of the roadway surrounding rock system.

[0019] Based on the tunnel cross-sectional dimensions and geological survey data, a geometric model containing the surrounding rock entity is established and subjected to mesh discretization; the physical and mechanical parameters and yield criteria of the surrounding rock material are defined, the global stiffness matrix is ​​assembled, and corresponding displacement boundary conditions and initial geostress fields are applied to form the mechanical system to be analyzed.

[0020] S20 performs a diagnosis of unbalanced force fields in surrounding rock based on the principle of minimum plastic residual energy.

[0021] The unloading process of tunnel excavation is simulated, and the strain increment and elastic test stress of each element are calculated. For elements exceeding the yield surface, the true stress state that satisfies the constitutive relation is solved according to the principle of minimum plastic residual energy. The plastic stress increment is calculated and mapped to the nodal unbalanced force vector through element integration, thereby constructing an unbalanced force field that reflects the degree of local damage to the surrounding rock and the reinforcement requirements.

[0022] S30 generates an initial support scheme based on the characteristic parameters of the unbalanced force field.

[0023] The distribution characteristics of the unbalanced force vector at the nodes in the area to be supported are extracted to analyze the area's reinforcement requirements. The anchor length is determined based on the attenuation law of the unbalanced force along the depth of the surrounding rock. The anchor support density and spacing are determined based on the ratio of the total unbalanced force modulus of the area to the ultimate bearing capacity of a single anchor. The initial installation angle of the anchor is determined based on the opposite direction of the local unbalanced force vector, thus obtaining a set of initial support parameters with clear physical meaning.

[0024] S40, Establish a strong coupling analysis model for anchor bolt surrounding rock that considers interfacial bonding and slip behavior.

[0025] As a virtual unit, the anchor bolt is introduced into the bond-slip constitutive relation describing the nonlinear shear behavior of the interface between the anchor bolt and the surrounding rock. The relative slip variable and contact virtual work are defined, and the corresponding contact stiffness matrix is ​​derived. The contact stiffness matrix is ​​superimposed on the total stiffness matrix of the surrounding rock system to construct an incremental equilibrium equation set that can characterize the cooperative deformation mechanism between the support component and the surrounding rock.

[0026] S50, construct a multi-dimensional comprehensive objective function that includes mechanical and economic indicators.

[0027] The residual unbalanced force norm, which characterizes the stability of the surrounding rock, the displacement of the characteristic point, which characterizes the deformation control, the axial force state of the anchor bolt, which characterizes the safety of the components, and the material cost, which characterizes the project cost, are selected as evaluation dimensions. Through normalization and weighted summation, a comprehensive fitness function is established to quantitatively evaluate the merits of the support scheme.

[0028] S60 performs global optimization of support parameters based on an improved particle swarm optimization algorithm.

[0029] The length, spacing, installation angle, and preload of the anchor bolts are defined as optimization variables and encoded to initialize the particle population. The comprehensive fitness function value is used as the evaluation criterion to drive the particle population to iteratively search in the multidimensional parameter space according to the velocity and position update formulas. The boundary handling mechanism is used to constrain the range of variables, and the updated parameters are fed back to the coupled model for iterative solution until the unbalanced force of the surrounding rock is less than a given threshold, thus obtaining the globally optimal particle.

[0030] S70 decodes and outputs the globally optimal support parameters.

[0031] After the optimization is completed, the position vector corresponding to the global optimal particle is extracted, and it is decoded into specific anchor bolt length, spacing and angle values. After verification, it is used as the final roadway support design scheme.

[0032] The technical principles behind the above steps will be explained in detail below, combining mathematical formulas and specific implementation details.

[0033] See attached document Figure 2 When performing step S10 to construct the initial finite element numerical model of the roadway surrounding rock system, the specific implementation process includes: S101. Establish the tunnel's geometric model and perform spatial discretization. Based on geological survey data, construct a three-dimensional geometric entity. Use a finite element mesh generation algorithm to discretize the continuous geometric entity into a mesh model composed of nodes and elements. To balance computational accuracy and efficiency, high-density eight-node hexahedral elements are used for meshing in stress concentration areas around the tunnel.

[0034] S102, Assemble the stiffness matrix and establish the equilibrium equations. Based on the principle of virtual work, the strain energy within each element volume is integrated to obtain the element stiffness matrix, which is then assembled into a global stiffness matrix according to the nodal topology. Based on this, a set of algebraic equations describing the equilibrium relationship between the nodal displacements and the stiffness matrix under external loads is established as the basic framework for subsequent nonlinear iterations: ; In the formula, Represents the global stiffness matrix of the surrounding rock system; This represents the global nodal displacement vector of the surrounding rock to be solved; This represents the external load vector.

[0035] S103, Apply boundary conditions and initial geostress. Apply displacement constraints to the model boundaries and apply the initial geostress tensor at the integration point based on the original rock stress test data. Eliminate artificial spurious deformations through geostress equilibrium calculations.

[0036] See attached document Figure 3 In performing step S20, the excess stress of the surrounding rock is essentially extracted through numerical calculation. This process includes: S201, Calculation of elastic test stress and yield criterion. Simulation of excavation unloading, assuming the material remains linearly elastic, calculates the elastic test stress. Utilizing the yield criterion function... Verification, if If the stress level is too high, the point is considered to have entered a plastic state and stress adjustment is required.

[0037] S202, solves for the plastic stress difference based on the principle of minimum plastic residual energy. For the integration point determined to be yielding, find the true stress located on the yield surface. This makes the actual stress and the elastic test stress... Plastic complementary residual energy increment between Minimize. The mathematical expression of this optimization problem is as follows: ; In the formula, Represents the overall plastic residual energy of the structure; Represents the material flexibility tensor; For elastic test stress tensor; It is the true stress tensor; The unit volume is denoted as .

[0038] By solving this variational problem (i.e., the closest point projection method), the plastic stress difference tensor is obtained. .

[0039] S203 maps the plastic stress difference to a nodal unbalanced force vector. To transform the stress tensor into a vector force that can guide support design, the principle of virtual work is used to transform the integral of the plastic stress difference within the element into an equivalent nodal force: ; In the formula, This represents the unbalanced force vector at the element node; This is the transpose of the strain-displacement matrix.

[0040] By assembling and superimposing the nodal forces of all units according to their node numbers, a global nodal unbalanced force field is formed. The physical significance of this force field lies in quantitatively indicating the size of the gap in the self-supporting capacity of the surrounding rock and the direction of the required external support force.

[0041] When performing step S30, the specific steps include: S301, Analysis of the total demand for surrounding rock reinforcement area.

[0042] In the area awaiting support Internally, the depth of plastic influence and effective anchorage length are determined by searching the radial distribution of unbalanced forces at the nodes. Specifically, values ​​are taken at each node inside the surrounding rock along the tunnel normal, and recorded along the depth... Unbalanced force modulus Find the minimum depth value that satisfies the following formula: ; In the formula, This represents the maximum unbalanced force in the region. This is the attenuation coefficient (e.g., 0.1).

[0043] Let this depth be the depth of influence. The initial effective anchorage length is then taken as ,in For safety margin.

[0044] Simultaneously, the calculation of the direction of stability imbalance and the normal reinforcement requirement are differentiated. First, the vector sum of the unbalanced force vectors at all nodes within the region is calculated. The opposite direction of this vector is the optimal support force direction for the surrounding rock in this area.

[0045] Subsequently, the resultant force was calculated in the normal direction at the tunnel surface. The projection onto the surface yields the total required force for regional normal reinforcement. : ; In the formula, For the first The unbalanced force vector at each node; This is the vector of the total resultant force of the unbalanced forces in the region (used for subsequent angle determination); This is for the normal scalar requirement (used to determine the number of roots later).

[0046] S302, determine the ultimate bearing capacity of a single anchor bolt.

[0047] The effective bearing capacity of a single anchor bolt must consider both the strength of the bolt material and the bonding capacity of the anchorage interface, taking the smaller value of the two as the design basis. The calculation formula is as follows: ; In the formula, This is a comprehensive adjustment factor; The yield force of the anchor rod; The ultimate bond strength at the interface of the anchorage section; These are the corresponding resistance partial factors.

[0048] S303, Analysis of Anchor Bolt Support Density and Angle.

[0049] Based on the regional normal total reinforcement requirements and the bearing capacity of a single anchor bolt Calculate the theoretical total number of anchor bolts required to maintain regional stability. And round up: ; Based on the total number of roots and reinforced zoning surface area By reverse calculation, the uniform spacing and row spacing of the anchor bolts can be obtained.

[0050] Specifically, the initial installation angle of the anchor bolt is set to the resultant vector of the total unbalanced force in the region calculated in step S301. In the opposite direction, to achieve precise countermeasure against the main sliding trend of the surrounding rock.

[0051] When performing step S40, the specific steps include: S401 defines the interface behavior and coupling equations. Virtual anchor elements that can be dynamically adjusted according to parameters are introduced, and a nonlinear constitutive model (such as a bi-exponential model or a tri-segmented model) is established to describe the relative slippage between the anchor and the surrounding rock interface.

[0052] In this embodiment, a modified double-exponential bond-slip constitutive model is preferably used, the expression of which is: ; The bond strength function during the softening stage Defined as: ; In the formula, This indicates relative sliding of the interface. Indicates interfacial shear force. Indicates the coefficient of friction. Normal compressive stress, For residual strength, These are the fitting parameters. Based on this constitutive pair The tangential contact stiffness can be obtained by differentiation and used for assembly. .

[0053] The corresponding interface tangential stiffness is calculated. Based on the principle of virtual work, the incremental equilibrium equations of the system, including the degrees of freedom of the surrounding rock, the degrees of freedom of the anchor bolt, and the interface coupling effect, are derived: ; In the formula, Represents the rock mass stiffness matrix. Represents the anchor stiffness matrix. Represents the contact stiffness matrix. , This represents the increment of rock mass node displacement and slippage in this iteration. This represents the internal force vector of the anchor bolt and the surrounding rock. This represents the external force vectors of the anchor bolt and the surrounding rock; The shape function mapping matrix; It is a rotation matrix; This is the interface shear force vector.

[0054] S402, Solve the discrimination. Solve the above system of equations to calculate the vector norm of the residual nodal unbalanced forces in the surrounding rock. Determine if the condition is met. ( (This is a preset threshold). If the threshold is met, the current support parameters are determined to be the optimal solution, the optimization is terminated directly, and the result is output. If the threshold is not met, it means that the current solution has not yet achieved an ideal equilibrium state for the surrounding rock, and optimization needs to be performed in S50 and subsequent steps.

[0055] When performing step S50, the specific steps include: S501, Quantitative sub-evaluation indicators. Calculate the deformation index (normalized maximum displacement) for each scheme separately. ), force index (normalized maximum unbalanced force) Safety indicators (normalized anchor bolt axial force) ) and cost indicators (normalized material cost) ).

[0056] S502, Establish the comprehensive fitness function. Combine the above-mentioned sub-indicators through a weighted summation to form a scalar objective function that drives the optimization algorithm. This function directly reflects the trade-off between security, stability, and economy in the proposed solution: ; In the formula, This represents the maximum axial force of the anchor bolt. The anchor rod's yield strength; This indicates the allowable convergence deformation limit; Indicates design reference value; These are the weighting coefficients. The denominators above are the corresponding reference thresholds or normalized baseline values. Minimizing this objective function corresponds to the search objective of the optimal support scheme.

[0057] When performing step S60, the specific steps include: S601, Initialization and Update Mechanism. Parameters such as anchor bolt length, spacing, and preload are encoded into design vectors. These correspond to the anchor bolt lengths, circumferential spacing, axial spacing, anchor bolt inclination angles, and preload of the top / side / bottom plates, respectively. During the iteration process, the population is initialized using the analytical solution from step S30. For each particle, based on its historical best position... and global optimal position Update its speed The updated formula is as follows: ; In the formula, Indicates the first Generation, First The particle, the first The speed of each variable Indicates location, This indicates the best position in the particle's history. Indicates the best position in the global history; The inertial weights decrease linearly with the number of iterations and are used to balance global and local search capabilities.

[0058] S602 handles the boundary constraints of the search space. To ensure that the generated support parameters are within the allowable range of engineering (e.g., the anchor spacing cannot be too small), an instant boundary handling strategy is adopted. When the particle update position exceeds the preset range... When necessary, force corrections will be made: ; ; After obtaining the revised new support parameters, the program will return to step S40 with the new parameter set, update the properties (stiffness matrix) of the virtual anchor element, solve the incremental equilibrium equation again and calculate the new unbalanced force of the surrounding rock, forming a closed loop iteration, until the calculated unbalanced force is less than the given threshold (i.e., the criterion of S402 is met) and stop the optimization.

[0059] When performing step S70, the specific steps include: The globally optimal position vector is extracted and decoded into specific parameters conforming to the engineering modulus (such as multiples of 0.1 meters in spacing) through nearest neighbor mapping and directional rounding strategies. The decoded scheme is then verified using the strength reduction method to calculate the system safety factor. If the verification passes, a final report output containing a 3D topology model, technical parameters, and a bill of materials is generated. It also supports feeding back on field monitoring data to the numerical model, correcting constitutive parameters and triggering a new round of S20 to S70 processes, thereby achieving closed-loop rolling optimization of the support scheme.

Claims

1. A method for intelligent optimization of roadway anchor bolt group support parameters based on unbalanced forces, characterized in that, include: S10, Construct the initial finite element model of the surrounding rock; Geometric entities are established based on geological data and discretized into meshes. Material parameters and yield criteria are defined, a global stiffness matrix is ​​assembled, displacement boundaries and initial geostress fields are applied, and a mechanical system to be analyzed is formed. S20, perform unbalanced force field diagnosis; simulate excavation and unloading using the mechanical system to be analyzed, solve the true stress state for the over-yielding element according to the principle of minimum plastic residual energy, calculate the plastic stress increment, and map it to the nodal unbalanced force vector through element integration to construct an unbalanced force field that reflects local damage and reinforcement requirements. S30, Generate an initial scheme; Extract node distribution characteristics based on the unbalanced force field, analyze regional reinforcement requirements, determine anchor length, spacing and angle, and obtain the initial support parameter set; S40, Establish a coupled analysis model; the anchor bolt is used as a virtual unit, and the bond-slip constitutive relation describing the nonlinear shear behavior of the anchor bolt-surrounding rock interface is introduced. The contact stiffness matrix is ​​derived and superimposed on the global stiffness matrix. An incremental equilibrium equation set characterizing the cooperative deformation mechanism is constructed. The equation set is solved to obtain the support effect of this support scheme on the surrounding rock, and it is determined whether the unbalanced force of the surrounding rock is less than a given threshold. If the unbalanced force is less than the given threshold, the current support scheme is output as the optimal support parameters; otherwise, the following steps are executed. S50, Construct the comprehensive objective function; The residual unbalanced force norm, characteristic point displacement, anchor bolt axial force, and material cost are selected, and a comprehensive fitness function is established by normalization and weighted summation. S60, perform global optimization; encode the support parameters, initialize the particle population using the initial support parameter set, drive the particles to iteratively search in multidimensional space based on the incremental balance equation set and the comprehensive fitness function, and use the boundary mechanism constraint to obtain new support parameters. Re-enter the virtual anchor element to calculate the unbalanced force in a loop until the unbalanced force is less than the given value, and then stop the optimization to give the optimal particle. S70, output the optimal parameters; extract the position vector corresponding to the globally optimal particle, decode it into a specific value, verify it, and output it as the final solution.

2. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 1, characterized in that, S10 specifically includes: Based on the geological data, a three-dimensional geometric entity is constructed. In the stress concentration area around the tunnel, an eight-node hexahedral element is used to divide the three-dimensional geometric entity, and the three-dimensional geometric entity is discretized into a mesh model composed of nodes and elements. The assembly of the global stiffness matrix specifically includes: integrating the strain energy within each unit volume based on the principle of virtual work to obtain the unit stiffness matrix, and assembling the unit stiffness matrix into the global stiffness matrix of the mechanical system to be analyzed according to the node topology relationship.

3. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 1, characterized in that, In step S20, the specific steps for solving the true stress state of the super-yielding element based on the principle of minimum plastic residual energy and calculating the plastic stress increment include: Assume the material maintains the elastic trial stress of the linear elastic calculation unit; For the integration point that is determined to be yielding by the elastic test stress, find a true stress tensor located on the yield surface such that the plastic complementary residual energy increment between the true stress tensor and the elastic test stress is minimized. The difference between the elastic test stress and the actual stress tensor is calculated to obtain the plastic stress difference tensor as the plastic stress increment.

4. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 3, characterized in that, In step S20, the step of constructing an unbalanced force field reflecting local damage and reinforcement requirements by mapping element integrals to nodal unbalanced force vectors specifically includes: Based on the principle of virtual work, the integral of the plastic stress difference tensor inside the unit is transformed into the unbalanced force vector of the unit node; The unbalanced force vectors of all unit nodes are assembled and superimposed according to the node number to form the unbalanced force field; The unbalanced force field quantitatively indicates the size of the gap in the self-supporting capacity of the surrounding rock and the direction of the required external support force.

5. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 4, characterized in that, In step S30, determining the anchor bolt length based on the node distribution characteristics extracted from the unbalanced force field specifically includes: Search for the radial distribution of nodal unbalanced force vectors within the area to be supported, and record the unbalanced force modulus along the depth of the surrounding rock. Find the minimum depth value at which the unbalanced force modulus satisfies the attenuation coefficient requirement, and use the minimum depth value as the basis to determine the length of the anchor rod.

6. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 1, characterized in that, In step S30, the reinforcement requirements for the analysis area, specifically determining the anchor spacing and angle, include: Calculate the resultant force vector of all unbalanced force vectors of the nodes in the area to be supported, and calculate the projection of the resultant force vector onto the normal direction of the roadway surface to obtain the total required force for the normal reinforcement of the area; The total number of anchor bolts required is established based on the ratio of the total required force for the normal reinforcement of the area to the ultimate bearing capacity of a single anchor bolt, and the anchor bolt spacing is calculated in reverse. The initial installation angle of the anchor bolt is determined based on the opposite direction of the resultant force vector described locally.

7. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 1, characterized in that, In S40, the anchor bolt is treated as a virtual element, and the bond-slip constitutive relation adopts a double-exponential bond-slip constitutive model: The bi-exponential bond-slip constitutive model includes a bond strength function describing the softening stage; The derivation of the contact stiffness matrix includes: obtaining the interface tangential stiffness by differentiating the interface relative slip in the double exponential bond-slip constitutive model, and assembling the contact stiffness matrix based on the interface tangential stiffness.

8. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 1, characterized in that, In step S50, the specific steps for establishing the comprehensive fitness function include: The normalized maximum displacement, normalized maximum unbalanced force, normalized anchor axial force, and normalized material cost of the residual unbalanced force norm, characteristic point displacement, anchor axial force, and material cost are calculated respectively as four normalized indicators. The four normalized indices are combined by weighted summation to form the comprehensive fitness function, which directly reflects the trade-off between safety, stability, and economy of the scheme.

9. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 1, characterized in that: In S60, the specific strategy for constraining the range of variables using the boundary mechanism is as follows: When the particle update position exceeds the preset range in order to obtain new support parameters, the particle update position is forcibly corrected. If the particle update position is less than the lower bound, the particle update position is set to the lower bound and the particle velocity is set to zero; If the particle update position is greater than the upper bound, the particle update position is set to the upper bound and the particle velocity is set to zero.

10. The intelligent optimization method for roadway anchor bolt group support parameters based on unbalanced forces according to claim 1, characterized in that, Specifically, S70 includes: Extract the position vector corresponding to the globally optimal particle, and decode the position vector into specific parameters that conform to the engineering modulus through nearest neighbor mapping and directional rounding strategy; The specific parameters after decoding are verified using the strength reduction method, and the system security factor is calculated. After verifying the system's safety factor, a report containing a three-dimensional topology model and a bill of materials is generated as the final solution output.

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