Method for determining rock arch resistance height of soft and hard alternating stratum tunnel, firmware chip

Abstract

The application provides a method for determining the rock arch resistance height of a soft and hard alternating stratum tunnel and a firmware chip, relates to the technical field of tunnel engineering stability analysis and safety design, can combine the resistance failure mechanism of the key hole top part of the soft and hard alternating stratum tunnel, respectively consider the mechanical properties such as the elastic modulus, the cohesive force, the internal friction angle, the joint strength and the non-constant strength parameters of the soft layer and the hard layer, accurately depict the sequence characteristics and the spatial distribution of the soft and hard alternating stratum, so as to more truly reflect the load transmission path, the stress distribution law and the potential failure mode, and significantly improve the engineering fitting degree and the reliability of the calculation result. The application realizes the quantitative analysis of the supporting effect, takes the supporting stress as a clear external force component into the energy balance system, can quantitatively evaluate the influence of different supporting stresses on the rock arch resistance height, and provides a theoretical basis and a practical tool for the fine design and economic optimization of the supporting scheme.

Description

Technical Field

[0001] This invention relates to the field of stability analysis and safety in tunnel engineering, and in particular to a method for determining the resistance height of the rock arch in tunnels with alternating soft and hard strata, and a firmware chip. Background Technology

[0002] With the advancement of urban subway construction in my country, tunnel engineering inevitably needs to traverse various complex geological conditions. Among them, alternating soft upper and hard lower strata are a common and engineeringly unique geological combination. One of the core issues in the stability of subway tunnels built in such strata is how to scientifically determine the minimum rock arch resistance height from the tunnel arch to the surface of the underlying bedrock. If this thickness is too small, it can easily lead to catastrophic accidents such as instability and failure of the hard strata at the top of the tunnel, excessive surface subsidence, or even collapse; if the thickness is too large, it will lead to an increase in tunnel depth, significantly increasing project costs and construction difficulty.

[0003] Current traditional methods for calculating the resistance height of rock arches in subway tunnels still face the following technical bottlenecks: (1) The model is idealized but does not match the geological conditions: The interaction between soft and hard strata is inherently heterogeneous and anisotropic, with significant abrupt changes in strength and stiffness at the interface between the soft and hard surfaces. The idealized assumptions of traditional models cannot capture this abrupt effect, and the presupposed regular failure surfaces differ greatly from the complex slip surfaces actually generated during stratum instability, which are controlled by the stratum interface. This results in poor agreement between the calculation results and engineering practice.

[0004] (2) The analysis has only one dimension and does not consider energy dissipation: The instability and failure of composite strata is an energy-driven and energy-dissipating process. Traditional methods completely ignore the internal energy dissipation mechanisms during failure, failing to fully reveal the failure mechanism from the perspective of energy conservation. For composite strata with alternating hard and soft layers, different strata have different energy dissipation capacities, making analyses based solely on force balance incomplete.

[0005] (3) Highly empirical, lacking universality: Traditional methods are typically derived from specific engineering experience or simplified assumptions, containing a large number of empirical coefficients. These coefficients are highly dependent on specific regions or specific geological types. When geological conditions vary significantly, engineers need to select coefficients based on their personal experience, which is highly subjective, and the results calculated by different people may differ greatly, making it difficult to establish a unified and objective standard.

[0006] (4) The effects of tunnel failure surface shape and size cannot be taken into account: Traditional formulas typically simplify tunnels to circular or rectangular shapes and assume a simple linear relationship between the failure extent and tunnel size. However, the actual shape and size of the failure surface of a tunnel significantly affect the stress redistribution and failure mode of the hard strata above the tunnel.

[0007] (5) The stress treatment of the support is simplified and based on experience, making quantitative analysis impossible: Because support stress cannot be precisely quantified, engineers often adopt conservative support schemes in their designs, leading to excessively high support costs or, conversely, safety risks due to inadequate design. This experience-based approach lacks economic optimization, making support cost control lack a scientific basis and making it difficult to find a balance between safety and economy.

[0008] (6) The strength model is too simplified and cannot reflect the unsteady characteristics of the material that fails: Traditional methods generally use the Mohr-Coulomb criterion, which uses a linear strength envelope to approximate the shear strength of soil and rock materials. This criterion is difficult to effectively describe the unsteady and unstable failure characteristics of the strata surrounding the tunnel after excavation in soft and hard strata.

[0009] Therefore, it is necessary to provide a method for determining the resistance height of rock arches in tunnels with soft and hard interaction between strata, and firmware chips to solve the above problems. Summary of the Invention

[0010] The purpose of this invention is to establish a method and firmware chip for determining the resistance height of rock arches in tunnels with soft and hard interaction strata. This method replaces force balance with energy balance, replaces subjective assumptions with optimization solutions, and uses unsteady instability energy release functions to describe rock and soil failure. It establishes a comprehensive design method that meets both the safety and economic requirements of tunnel support, thus solving the problems existing in the prior art.

[0011] To achieve the above objectives, the present invention provides a method for determining the resistance height of the rock arch in tunnels in soft-hard interactive strata, comprising the following steps: S1: Conduct on-site geological exploration and lithology identification, explore the boundary between the upper soft strata and the lower hard strata, obtain original, undisturbed samples of the upper soft strata and the lower hard strata, conduct physical and mechanical parameter experiments, and determine the physical property index parameters and strength and deformation index parameters of the upper soft strata and the lower hard strata respectively. S2: Based on the conditions of the upper soft strata and the lower hard strata, combined with the cross-sectional design parameters of the tunnel, a rock arch resistance analysis model for the tunnel top is constructed, and support stress is set at the bottom of the resistance zone. ; S3: Utilizing the unsteady instability energy release function of the damaged material within the resistance failure zone, the partial derivative of the stress at any point within the failure zone is calculated. Combined with deformation geometry, the normal stress deformation index at any point within the resistance failure zone is then calculated. and shear stress deformation index The unsteady instability energy release function is as follows: ; in, , , K , m This is an empirical coefficient, with a value range of 0 to 1; The compressive strength of hard strata materials, The tensile strength of the hard formation material is obtained experimentally through the physical and mechanical parameters in S1. Based on the normal stress at any point within the resistance damage zone and shear stress The total energy released by the resistance zone is calculated by integrating along the entire resistance zone. : ; In the formula, Represents the spatial extent of the entire resistance zone, including its top boundary, and is the equation of the tunnel top profile surface. Boundary and resistance to failure surface equations boundary; Normal stress deformation index Shear stress deformation index ; In the formula, The calculation coefficients reflecting the plasticity of the material are obtained experimentally through the physical and mechanical parameters in S1; S4: Based on the spatial extent of the resistance zone and the action, type, and magnitude of external loads, solve for the failure components corresponding to each part of the resistance zone. Each failure component includes the failure component of the pressure in the upper weak strata. Gravity-induced damage component of hard strata and support resistance to stability maintenance ; S5: Total energy released from the resistance zone obtained in S3 Based on the failure components obtained in S4, an energy difference prediction function for resisting the instability and failure of the tunnel roof rock arch in the failure zone is constructed: ; S6: Equation of the resistance-to-failure surface obtained in S3 based on the energy difference prediction function obtained in S5. Solving for the variational problem, we obtain the variational extremum condition and boundary condition of the energy difference prediction function. The expression for the difference prediction function is given. The support stress in S2 is obtained by solving. Calculated value of corresponding tunnel arch resistance height ; S7: Construct a three-dimensional numerical calculation model in the simulation software corresponding to different rock arch resistance heights, and determine the relationship with support stress. Corresponding numerical simulation calculation values ​​of tunnel arch resistance height ; S8: Based on S6 And obtained from S7 Establish a quantitative evaluation index, Q, for the accuracy deviation rate of rock arch resistance height calculation results; S9: Repeat S2-S8 to obtain any support stress within the set range. Calculated value of corresponding rock arch resistance height Arbitrary support stress is obtained based on the cross-sectional design parameters of the mined tunnel. Corresponding support costs ; S10: The arbitrary support stress obtained in S9 Calculated value of corresponding rock arch resistance height Support costs Dimensionless processing was performed to establish a corresponding standardized evaluation index for the resistance height of the rock arch. and standardized evaluation indicators for support costs ; S11: Draw standardized evaluation indicators for the resistance height of rock arches Standardized evaluation indicators for support costs With support stress The curves change, and the horizontal axis of the intersection point represents the reasonable support stress that balances tunnel safety and support economy. The vertical axis of the intersection point represents the rock arch resistance height of the tunnel corresponding to the soft upper strata and the hard lower strata, as well as the reasonable support cost.

[0012] Preferably, the density value of the upper and middle weak strata in S1 is calculated by methods such as ring sample cutting, weighing, and drying. The density of the lower hard strata was calculated by measuring its dimensions and weighing it. Based on the density values ​​measured in the experiment and Multiply by the gravitational acceleration g to obtain the specific weight of the material; The physical and mechanical parameter experiments include uniaxial compression test, triaxial compression test, compression-shear test and Brazilian splitting test; Physical property parameters and strength / deformation parameters include compressive strength, tensile strength, and elastic modulus. Poisson's ratio, unsteady strength parameters, and plastic deformation parameters.

[0013] Preferably, the support stress in S2 Set along the normal direction inside the tunnel contour surface; The geometry of the failure surface, representing the area extending from the tunnel arch to the boundary between the upper soft strata and the lower hard strata, is described. Describe the geometry of the tunnel's top profile surface.

[0014] Preferably, the calculation process for each failure component in S4 is as follows: ; in, The pressure is transmitted from the soft strata above. To resist the deformation rate of the underlying hard stratum material within the damage range; ; in, The density of the underlying hard stratum material; .

[0015] Preferably, S7 specifically includes the following steps: S71: Based on the physical property index parameters and strength and deformation index parameters of the upper soft strata and the lower hard strata obtained in S1 and the cross-sectional design parameters of the mined tunnel obtained in S2, establish a three-dimensional numerical calculation model corresponding to different rock arch resistance heights. S72: Conduct tunnel excavation simulations with different rock arch resistance heights. After tunnel excavation, apply the same support stress as in S2 around the tunnel perimeter. Perform model calculations; S73: After the model calculation is completed, extract the settlement displacement values ​​of the tunnel top corresponding to different rock arch resistance heights; S74: Plot the curve of settlement displacement as a function of the rock arch resistance height. Determine the inflection point of the curve based on its trend. The rock arch resistance height corresponding to the inflection point is used as the value for numerical simulation calculation. .

[0016] Preferably, in S8, the tunnel arch resistance height is calculated based on the value obtained in S6. The numerical simulation values ​​obtained from S74 Calculate the evaluation indicators: .

[0017] When the evaluation index Q is less than 5%, the calculation results are reliable; when the index Q is greater than 5%, theoretical errors exist. and Adjustments and improvements were made until the evaluation indicator Q was less than 5%.

[0018] Preferred, S10 Standardized Evaluation Index for Rock Arch Resistance Height The calculation method is as follows: ; In the formula, This indicates the maximum calculated resistance height of the rock arch; This represents the minimum calculated resistance height of the rock arch; Standardized evaluation indicators for support costs The calculation method is as follows: ; In the formula, This represents the cost corresponding to the minimum support stress. This represents the cost corresponding to the maximum support stress; Indicates support stress The corresponding cost.

[0019] A firmware chip stores control instructions and is embedded in a tunnel engineering analysis device or a geomechanical parameter acquisition terminal. When the control instructions are executed, the firmware chip completes the steps in the comprehensive determination method of the resistance height of the tunnel arch in soft and hard interactive strata.

[0020] Therefore, the present invention employs the aforementioned method for determining the resistance height of rock arches in tunnels in soft-hard interactive strata, and the firmware chip, with the following technical effects: (1) This invention can combine the resistance to failure mechanism of the key tunnel top of the soft and hard strata tunnel, and consider the mechanical properties of the soft layer and hard layer respectively, such as elastic modulus, cohesion, internal friction angle, joint strength, unsteady strength parameters, etc., to accurately characterize the sequence characteristics and spatial distribution of the soft and hard alternating strata, thereby more realistically reflecting the load transfer path, stress distribution law and potential failure mode, and significantly improving the engineering consistency and reliability of the calculation results.

[0021] (2) The present invention adopts a multidimensional analysis strategy, organically combining force balance and energy principle to ensure that the destructive contribution of external load does not exceed the total energy released by the system, while satisfying energy conservation and maneuverability conditions, thus constructing a more rigorous and complete mechanical analysis framework, making the critical state sought closer to reality and providing higher safety assurance.

[0022] (3) This invention introduces a systematic energy release assessment into the resistance-to-damage zone to accurately quantify the different roles played by weak strata and hard rock strata during the damage process, thereby more realistically reflecting the actual stability state of composite strata and significantly improving the accuracy and reliability of safe thickness prediction. Furthermore, through computer system integration and modular architecture, the analysis process is digitized and automated, effectively avoiding subjective biases caused by differences in human experience or operational errors, and improving the consistency and credibility of the results.

[0023] (4) The present invention improves the method of determining the morphology of the failure surface by solving it as a surface function to be optimized, which significantly reduces the influence of subjective assumptions and enables the failure surface to adaptively evolve into the most dangerous slip fracture morphology according to the formation characteristics and stress state, which is more in line with the actual mechanical mechanism.

[0024] (5) This invention realizes the quantitative analysis of the support effect, incorporates the support stress as a clear external force component into the energy balance system, and can quantitatively evaluate the influence of different support stresses on the resistance height of the rock arch, providing a theoretical basis and practical tool for the refined design and economic optimization of the support scheme.

[0025] (6) The present invention uses an industry-recognized unsteady instability energy release function to describe the deformation and failure behavior of rock and soil geological materials, which can more accurately reflect the unsteady failure characteristics of the surrounding rock than the traditional Mohr-Coulomb criterion.

[0026] (7) This invention proposes a dimensionless evaluation index that can combine tunnel support safety and support economy, which breaks through the traditional insufficiency of comprehensive quantitative evaluation of different unit dimensions, and provides a quantitative basis for tunnel support safety and economic design. Attached Figure Description

[0027] Figure 1 This is the tunnel resistance to damage analysis model in Embodiment 4 of the present invention; Figure 2 This is a graph showing the relationship between settlement displacement and rock arch resistance height in Embodiment 4 of the present invention; Figure 3 The curves of the standardized evaluation index of rock arch resistance height and the standardized evaluation index of support cost as a function of support stress in Embodiment 4 of the present invention are shown. Figure 4 This is a flowchart of the method for determining the resistance height of the rock arch in a tunnel with alternating soft and hard strata in this invention. Detailed Implementation

[0028] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0029] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0030] Example 1 like Figure 4 As shown, this invention provides a method for determining the resistance height of a tunnel arch in soft-hard interactive strata, comprising the following steps: S1: Conduct on-site geological exploration and lithology identification. Through borehole exploration, determine the boundary between the upper soft strata and the lower hard strata. Within the planned tunnel area, based on the tunnel depth and geological conditions, use rotary drilling technology and a hydraulic core drilling rig to conduct borehole exploration. While ensuring the integrity of the core samples, accurately determine the boundary between the upper soft strata and the lower hard strata. Obtain pristine, undisturbed samples of the upper soft strata and the lower hard strata, and conduct physical and mechanical parameter experiments to determine the physical properties and strength / deformation parameters of the upper soft strata and the lower hard strata, respectively. The density of the upper and middle weak strata in S1 was calculated by cutting, weighing, and drying the samples using a ring sampler. The density of the lower hard strata was calculated by measuring its dimensions and weighing it. Based on the density values ​​measured in the experiment and Multiply by the gravitational acceleration g to obtain the specific weight of the material; The physical and mechanical parameter experiments include uniaxial compression test, triaxial compression test, compression-shear test and Brazilian splitting test; Physical property parameters and strength deformation parameters include compressive strength, tensile strength, and elastic modulus. Poisson's ratio, unsteady strength parameters, and plastic deformation parameters.

[0031] S2: Based on the conditions of the upper soft strata and the lower hard strata, combined with the cross-sectional design parameters of the tunnel, a rock arch resistance analysis model for the tunnel top is constructed, and support stress is set at the bottom of the resistance zone. S2 Support Stress Set along the normal direction inside the tunnel contour surface; The geometry of the failure surface, representing the area extending from the tunnel arch to the boundary between the upper soft strata and the lower hard strata, is described. Describe the geometry of the tunnel's top profile surface.

[0032] S3: Utilizing the unsteady instability energy release function of the damaged material within the resistance failure zone, it is assumed that both the soft and hard strata within this region behave as ideal plastic materials at the instant of instability failure. The hard strata material within the resistance failure zone deforms at a rate... v Displacement or plastic deformation occurs within the tunnel. The partial derivative of the stress at any point within the failure zone is calculated, and combined with the deformation geometry, the normal stress deformation index resisting the stress at any point within the failure zone is calculated. and shear stress deformation index The unsteady instability energy release function is as follows: ; in, , , K , m This is an empirical coefficient, with a value range of 0 to 1; The compressive strength of hard strata materials, The tensile strength of the hard formation material is obtained experimentally through the physical and mechanical parameters in S1. Based on the compression-shear test obtained in S1, different normal stresses were obtained. Material failure shear stress under the corresponding conditions A pre-defined unsteady instability energy release function is adopted. For all ( The data is fitted; parameters are obtained using numerical optimization methods. The values ​​of K and m determine the unsteady instability release function. By minimizing the sum of squared residuals across all data points, the corresponding expression for the unsteady instability energy release function can be determined after fitting, along with the relevant expression. The magnitudes of the parameters K and m.

[0033] Based on the normal stress at any point within the resistance damage zone and shear stress The total energy released by the resistance zone is calculated by integrating along the entire resistance zone. : ; In the formula, where, Represents the spatial extent of the entire resistance zone, including its top boundary, and is the equation of the tunnel top profile surface. Boundary and resistance to failure surface equations boundary; Normal stress deformation index Shear stress deformation index ; In the formula, The calculation coefficients reflecting the plasticity of the material are obtained experimentally through the physical and mechanical parameters in S1; S4: Based on the spatial extent of the resistance zone and the action, type, and magnitude of external loads, solve for the failure components corresponding to each part of the resistance zone. Each failure component includes the failure component of the pressure in the upper weak strata. Gravity-induced damage component of hard strata and support resistance to stability maintenance ; The calculation process for each failure component in S4 is as follows: ; in, The pressure is transmitted from the soft strata above. To resist the deformation rate of the underlying hard stratum material within the damage range; ; in, The density of the underlying hard stratum material; .

[0034] S5: Total energy released from the resistance zone obtained in S3 Based on the failure components obtained in S4, an energy difference prediction function for resisting the instability and failure of the tunnel roof rock arch in the failure zone is constructed: ; Energy difference prediction function It's about destroying surfaces. The functional, predicted by the energy difference function right By solving the variational problem and applying the variational extremum conditions and the geometric boundary conditions corresponding to the boundary of the resistance-to-failure zone, the equation of the resistance-to-failure surface can be derived. .

[0035] The energy difference prediction function characterizes the difference between the total energy released by the entire system and the contribution or resistance component generated by all external loads when the hard strata in the resistance failure zone undergoes overall instability failure, reflecting the magnitude of energy dissipation generated in the entire resistance failure zone.

[0036] S6: Equation of the resistance-to-failure surface obtained in S3 based on the energy difference prediction function obtained in S5. Solving for the variational problem, we obtain the variational extremum condition and boundary condition of the energy difference prediction function. The expression for the difference prediction function is given. The support stress in S2 is obtained by solving. Calculated value of corresponding tunnel arch resistance height ; S7: Construct a three-dimensional numerical calculation model in the simulation software corresponding to different rock arch resistance heights, and determine the relationship with support stress. Corresponding numerical simulation calculation values ​​of tunnel arch resistance height ; S7 specifically includes the following steps: S71: Based on the physical property index parameters and strength and deformation index parameters of the upper soft strata and the lower hard strata obtained in S1 and the cross-sectional design parameters of the mined tunnel obtained in S2, establish a three-dimensional numerical calculation model corresponding to different rock arch resistance heights. S72: Conduct tunnel excavation simulations with different rock arch resistance heights. After tunnel excavation, apply the same support stress as in S2 around the tunnel perimeter. Perform model calculations; S73: After the model calculation is completed, extract the settlement displacement values ​​of the tunnel top corresponding to different rock arch resistance heights; S74: Plot the curve of settlement displacement as a function of the rock arch resistance height. Determine the inflection point of the curve based on its trend. The rock arch resistance height corresponding to the inflection point is used as the value for numerical simulation calculation. .

[0037] S8: Based on S6 And obtained from S7 Establish a quantitative evaluation index, Q, for the accuracy deviation rate of rock arch resistance height calculation results; The tunnel arch resistance height calculated in S8 is based on the value obtained in S6. The numerical simulation values ​​obtained from S74 Calculate the evaluation indicators: .

[0038] When the evaluation index Q is less than 5%, the calculation results are reliable; when the index Q is greater than 5%, theoretical errors exist. and Adjustments and improvements were made until the evaluation indicator Q was less than 5%.

[0039] S9: Repeat S2-S8 to obtain any support stress within the set range. Calculated value of corresponding rock arch resistance height Arbitrary support stress is obtained based on the cross-sectional design parameters of the mined tunnel. Corresponding support costs ; S10: The arbitrary support stress obtained in S9 Calculated value of corresponding rock arch resistance height Support costs Dimensionless processing was performed to establish a corresponding standardized evaluation index for the resistance height of the rock arch. and standardized evaluation indicators for support costs ; S10 Standardized Evaluation Index of Rock Arch Resistance Height The calculation method is as follows: ; In the formula, This indicates the maximum calculated resistance height of the rock arch; This represents the minimum calculated resistance height of the rock arch; Standardized evaluation indicators for support costs The calculation method is as follows: ; In the formula, This represents the cost corresponding to the minimum support stress. This represents the cost corresponding to the maximum support stress; Indicates support stress The corresponding cost.

[0040] S11: Draw standardized evaluation indicators for the resistance height of rock arches Standardized evaluation indicators for support costs With support stress The curves change, and the horizontal axis of the intersection point represents the reasonable support stress that balances tunnel safety and support economy. The vertical axis of the intersection point represents the rock arch resistance height of the tunnel corresponding to the soft upper strata and the hard lower strata, as well as the reasonable support cost.

[0041] A firmware chip stores control instructions and is embedded in a tunnel engineering analysis device or a geomechanical parameter acquisition terminal. When the control instructions are executed, the firmware chip completes the steps in the comprehensive determination method of the resistance height of the tunnel arch in soft and hard interactive strata.

[0042] Example 2 A stability analysis system for tunnel arches in soft-hard interactive strata is constructed based on a method for determining the resistance height of the rock arch. The system includes a geological information and mechanical parameter management module, a rock arch failure mechanism and energy analysis module, a critical state self-identification and safe thickness analysis module, a design verification and engineering application decision-making module, and a parameterized analysis and economic optimization module. The geological information and mechanical parameter management module integrates field exploration and laboratory test data to establish an information database that includes the interface between soft and hard strata and the physical and mechanical properties of soil and rock, providing a complete and reliable set of initial parameters for subsequent analysis.

[0043] The rock arch failure mechanism and energy analysis module automatically constructs a geometric model of the potential rock arch failure zone at the top of the tunnel based on an information database. Through the embedded unsteady instability energy release function and energy method calculation kernel, it solves the total internal energy release rate and all external action components of the failure zone during the instability process.

[0044] The critical state self-identification and safe thickness analysis module, based on the energy balance principle, uses variational optimization algorithms to adaptively search and determine the morphology of potential failure surfaces; by solving the control equations when the system is in a limit equilibrium state, it automatically outputs the theoretical value of the critical rock arch resistance height at the tunnel centerline.

[0045] The design verification and engineering application decision module automatically compares and verifies theoretical analysis results by driving external numerical simulation software; at the same time, it corrects the theoretical critical values ​​according to the preset safety level of the project, outputs recommended safety thickness to guide construction drawing design, and generates an analysis report containing failure modes and risk warnings.

[0046] The parametric analysis and economic optimization module is based on different support stresses. The theoretical calculation and numerical verification process is automatically repeated to obtain a series of theoretical rock arch resistance heights. and their corresponding numerical simulation values ;right and support costs Dimensionless processing is performed to generate standardized evaluation indicators for the resistance height of rock arches. Standardized evaluation indicators for support costs ;draw and The curves showing the changes in support stress are used to determine the optimal rock arch resistance height and support cost based on the intersection of the curves, providing a basis for decision-making on balancing engineering economy and safety.

[0047] Example 3 A tunnel safety assessment system includes a computing engine and a user terminal deployed on a cloud server. The computing engine receives engineering parameters uploaded from the user terminal, runs a method for determining the rock arch resistance height of the tunnel based on soft and hard interaction, automatically calculates the recommended rock arch resistance height and support scheme, and returns the results to the user terminal.

[0048] Example 4 Taking a subway tunnel project in a certain city as an example, this tunnel traverses alternating soft and hard strata, with a section length of approximately 1.2 km. The tunnel is designed as a circular shield tunnel with an outer diameter of 6.2 m and an inner diameter of 5.5 m. This method is proposed to calculate the rock arch resistance height at the top of the tunnel. The specific steps are as follows: Step 1: Determination of engineering geological conditions and parameters. According to the geological survey report, the strata traversed by the tunnel from top to bottom are: Upper soft strata: silty clay, with the following parameters: density ρ 1 = 1.9 g / cm 3 Severe =19kN / m 3 elastic modulus E 1 = 5.58 MPa, internal friction angle =19 ° Cohesion c =21kPa, tensile strength =10kPa.

[0049] The underlying hard bedrock is limestone, with the following parameters: density. ρ 2 = 2.5 g / cm 3 Uniaxial compressive strength =30MPa, geological strength index GSI =30, Disturbance Factor D =0.1, the model parameter is the unsteady strength constant of the rock mass, specifically set as: the brittleness and hardness of the rock mass relative to the intact rock block. m =7, the degree of strength reduction of the rock mass relative to the intact rock block. m b =0.504, unsteady strength constant of the rock mass s =0.00032, unsteady strength-shape parameter of rock mass a =0.5014.

[0050] Tunnel design parameters: half width of the rock arch =3.1m, corresponding to an outer diameter of 6.2m, geometric parameters: vertical distance of the tunnel arch. c 1 = 1.5m, uniformly distributed ground load D 1 = 80 kN / m 2 Thickness of the support structure D 2 = 0.3m.

[0051] Step 2: Construct a model of the rock arch at the top of the tunnel to resist damage.

[0052] The tunnel's upper layer is composed of soft strata, while the lower layer is composed of hard strata. Due to the tunnel's long and narrow structure, it can be simplified into a two-dimensional problem for analysis. Simplified to , Simplified to A certain support stress is set inside the tunnel. Based on the geological conditions of soft upper and hard lower layers and the design parameters of the tunnel cross-section, an analytical model for the resistance to damage zone can be constructed, such as... Figure 1 As shown in the figure, the top of the failure model represents the pressure transmitted from the weak strata, the bottom represents the set support stress, and the corresponding boundary extends from the tunnel shoulders to the boundary between the upper weak strata and the lower hard strata. This area is the corresponding resistance zone against failure.

[0053] Step 3: Solve for the total released energy based on the unsteady instability release function.

[0054] Based on indoor physical and mechanical parameter tests, the unsteady instability energy release function corresponding to the failure of the lower hard rock layer was determined. .

[0055] The normal stress at the fracture surface was calculated by transforming the unsteady instability energy release function and matching the deformation index. =1.2MPa, shear stress =0.8MPa, normal stress deformation index =0.001s -1 Shear stress deformation index =0.002s -1 .

[0056] The total released energy is obtained by integrating over the area of ​​resistance to destruction. .

[0057] Step 4: Calculate the components of the external load.

[0058] The volume of hard strata within the resistance-to-damage zone is V1 = 125 m³. 3 Hard strata with high gamma intensity r =25kN / m 3 Calculate the gravity failure component of hard strata ; The volume of the upper weak strata within the resistance-to-failure zone is V2 = 80 m³. 3 The unit weight of the weak strata is γ1 = 19 kN / m. 3 Calculate the pressure failure component of the upper weak strata. = .

[0059] The support stress is set at q = 5 kPa, and the support area is S = 19.5 m². 2 Support, resistance, and stability maintenance .

[0060] Step 5: Calculate the resistance height of the rock arch.

[0061] Constructing the energy difference prediction function In order to find the true failure surface, we will use the equations of the resistance failure surface. f ( x The shape of () is treated as an optimization problem. The energy difference prediction function is used to... f ( x By performing a functional variational solution, we can derive... f ( x The general solution of ) is: At this time, you can f ( x Substitute this into the energy difference prediction function L, and let... By performing mathematical transformations and solving equations, the rock arch resistance height at the tunnel centerline can be determined, i.e. .

[0062] Step 6: Set different support stresses to obtain the rock arch resistance height corresponding to any support stress.

[0063] The support stress is set from 5 kPa to 95 kPa. S2-S7 are repeated to obtain the rock arch resistance height corresponding to any support stress. At the same time, the support cost corresponding to different support stresses is obtained. The rock arch resistance height and corresponding support cost corresponding to some support stresses are listed in Table 1.

[0064] Table 1

[0065] Step 7: Numerical verification.

[0066] For each support stress Set the corresponding tunnel top rock arch resistance height in the model. Then, the tunnel excavation process was simulated, and the settlement displacement at the center point of the tunnel roof was monitored. By gradually decreasing the rock arch resistance height or increasing the load, the instability process of the rock arch at the tunnel roof was simulated, and the curve of settlement displacement versus rock arch resistance height was obtained. Figure 2 As shown, the settlement curve typically exhibits a reversal point, and the rock arch resistance height corresponding to this reversal point is the critical height for numerical simulation. .

[0067] With support stress For example, theoretical calculations yield... .

[0068] In the numerical simulation, when the resistance height of the rock arch is... At that time, the settlement displacement was When the height decreases to At that time, the settlement displacement increased significantly to The height of the inflection point is obtained by fitting the settlement curve. .

[0069] Calculate the deviation rate as a quantitative evaluation index Less than 5%, which meets the requirements.

[0070] Step 8: Dimensionless processing and determination of the optimal rock arch resistance height and optimal support cost.

[0071] Based on the theoretical rock arch resistance height obtained in step S9 and the corresponding support costs Dimensionless processing is performed to eliminate the influence of dimensions, and the best balance between safety and economy is sought under the same benchmark.

[0072] S10 Standardized Evaluation Index of Rock Arch Resistance Height and standardized evaluation indicators for support costs In the calculation formula (corresponding support stress) ), (corresponding support stress) ). (corresponding support stress) ), (corresponding support stress) ).

[0073] Obtain the stress of each support and The values ​​are shown in Table 2; Table 2

[0074] like Figure 3 As shown, standardized evaluation indices for the resistance height of rock arches are plotted in the same coordinate system. Standardized evaluation indicators for support costs With support stress The changing curves. The two curves intersect at a point, which represents the optimal balance between the rock arch's resistance height and support costs. (By...) Figure 3 It is known that the support stress corresponding to the intersection point is approximately At this point: The theoretical resistance height of the rock arch m, support cost Ten thousand yuan.

[0075] Therefore, for this engineering example, the recommended reasonable rock arch resistance height is: m, corresponding to the optimal support cost is The result, costing tens of thousands of yuan, achieved optimal economic efficiency for the support scheme while ensuring tunnel stability.

[0076] Therefore, this invention adopts the above-mentioned method for determining the resistance height of the rock arch in tunnels with alternating soft and hard strata, replaces force balance with energy balance, replaces subjective assumptions with optimized solutions, and uses unsteady instability energy release functions to describe the failure of the soil and rock mass. It establishes a comprehensive design method that can meet both the safety and economic requirements of tunnel support, which can not only prevent tunnel collapse and excessive deformation and accurately predict surface settlement, but also optimize support design and reduce construction risks and economic costs.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for determining the resistance height of a rock arch in a tunnel through alternating soft and hard strata, characterized in that, Includes the following steps: S1: Conduct on-site geological exploration and lithology identification, explore the boundary between the upper soft strata and the lower hard strata, obtain original, undisturbed samples of the upper soft strata and the lower hard strata, conduct physical and mechanical parameter experiments, and determine the physical property index parameters and strength and deformation index parameters of the upper soft strata and the lower hard strata respectively. S2: Based on the conditions of the upper soft strata and the lower hard strata, combined with the cross-sectional design parameters of the tunnel, a rock arch resistance analysis model for the tunnel top is constructed, and support stress is set at the bottom of the resistance zone. ; S3: Utilizing the unsteady instability energy release function of the damaged material within the resistance failure zone, the partial derivative of the stress at any point within the failure zone is calculated. Combined with deformation geometry, the normal stress deformation index at any point within the resistance failure zone is then calculated. and shear stress deformation index The unsteady instability energy release function is as follows: ； in, , , K , m This is an empirical coefficient, with a value range of 0 to 1; The compressive strength of hard strata materials, The tensile strength of the hard formation material is obtained experimentally through the physical and mechanical parameters in S1. Based on the normal stress at any point within the resistance damage zone and shear stress The total energy released by the resistance zone is calculated by integrating along the entire resistance zone. : ； In the formula, where, Represents the spatial extent of the entire resistance zone, including its top boundary, and is the equation of the tunnel top profile surface. Boundary and resistance to failure surface equations boundary; Normal stress deformation index Shear stress deformation index ; In the formula, The calculation coefficients reflecting the plasticity of the material are obtained experimentally through the physical and mechanical parameters in S1; S4: Based on the spatial extent of the resistance zone and the action, type, and magnitude of external loads, solve for the failure components corresponding to each part of the resistance zone. Each failure component includes the failure component of the pressure in the upper weak strata. Gravity-induced damage component of hard strata and support resistance to stability maintenance ; S5: Total energy released from the resistance zone obtained in S3 Based on the failure components obtained in S4, an energy difference prediction function for resisting the instability and failure of the tunnel roof rock arch in the failure zone is constructed: ； S6: Equation of the resistance-to-failure surface obtained in S3 based on the energy difference prediction function obtained in S5. Solving for the variational problem, we obtain the variational extremum condition and boundary condition of the energy difference prediction function. The expression for the difference prediction function is given. The support stress in S2 is obtained by solving. Calculated value of corresponding tunnel arch resistance height ; S7: Construct a three-dimensional numerical calculation model in the simulation software corresponding to different rock arch resistance heights, and determine the relationship with support stress. Corresponding numerical simulation calculation values ​​of tunnel arch resistance height ; S8: Based on S6 And obtained from S7 Establish a quantitative evaluation index, Q, for the accuracy deviation rate of rock arch resistance height calculation results; S9: Repeat S2-S8 to obtain any support stress within the set range. Calculated value of corresponding rock arch resistance height Arbitrary support stress is obtained based on the cross-sectional design parameters of the mined tunnel. Corresponding support costs ; S10: The arbitrary support stress obtained in S9 Calculated value of corresponding rock arch resistance height Support costs Dimensionless processing was performed to establish a corresponding standardized evaluation index for the resistance height of the rock arch. and standardized evaluation indicators for support costs ; S11: Draw standardized evaluation indicators for the resistance height of rock arches Standardized evaluation indicators for support costs With support stress The curves change, and the horizontal axis of the intersection point represents the reasonable support stress that balances tunnel safety and support economy. The vertical axis of the intersection point represents the rock arch resistance height of the tunnel corresponding to the soft upper strata and the hard lower strata, as well as the reasonable support cost.

2. The method for determining the resistance height of a tunnel arch in soft-hard alternating strata according to claim 1, characterized in that, The density of the upper and middle weak strata in S1 was calculated by cutting, weighing, and drying the samples using a ring sampler. The density of the lower hard strata was calculated by measuring its dimensions and weighing it. Based on the density values ​​measured in the experiment and Multiply by the gravitational acceleration g to obtain the specific weight of the material; The physical and mechanical parameter experiments include uniaxial compression test, triaxial compression test, compression-shear test and Brazilian splitting test; Physical property parameters and strength / deformation parameters include compressive strength, tensile strength, and elastic modulus. Poisson's ratio, unsteady strength parameters, and plastic deformation parameters.

3. The method for determining the resistance height of a tunnel arch in soft-hard alternating strata according to claim 1, characterized in that, S2 Support Stress Set along the normal direction inside the tunnel contour surface; The geometry of the failure surface, representing the area extending from the tunnel arch to the boundary between the upper soft strata and the lower hard strata, is described. Describe the geometry of the tunnel's top profile surface.

4. The method for determining the resistance height of a tunnel arch in soft-hard alternating strata according to claim 1, characterized in that: The calculation process for each failure component in S4 is as follows: ； in, The pressure is transmitted from the soft strata above. To resist the deformation rate of the underlying hard stratum material within the damage range; ； in, The density of the underlying hard stratum material; 。 5. The method for determining the resistance height of a tunnel arch in soft-hard alternating strata according to claim 1, characterized in that, S7 specifically includes the following steps: S71: Based on the physical property index parameters and strength and deformation index parameters of the upper soft strata and the lower hard strata obtained in S1 and the cross-sectional design parameters of the mined tunnel obtained in S2, establish a three-dimensional numerical calculation model corresponding to different rock arch resistance heights. S72: Conduct tunnel excavation simulations with different rock arch resistance heights. After tunnel excavation, apply the same support stress as in S2 around the tunnel perimeter. Perform model calculations; S73: After the model calculation is completed, extract the settlement displacement values ​​of the tunnel top corresponding to different rock arch resistance heights; S74: Plot the curve of settlement displacement as a function of the rock arch resistance height. Determine the inflection point of the curve based on its trend. The rock arch resistance height corresponding to the inflection point is used as the value for numerical simulation calculation. .

6. The method for determining the resistance height of a tunnel arch in soft-hard alternating strata according to claim 5, characterized in that, The tunnel arch resistance height calculated in S8 is based on the value obtained in S6. The numerical simulation values ​​obtained from S74 Calculate the evaluation indicators: 。 When the evaluation index Q is less than 5%, the calculation results are reliable; when the index Q is greater than 5%, theoretical errors exist. and Adjustments and improvements were made until the evaluation indicator Q was less than 5%.

7. The method for determining the resistance height of a tunnel arch in soft-hard alternating strata according to claim 1, characterized in that, S10 Standardized Evaluation Index of Rock Arch Resistance Height The calculation method is as follows: ； In the formula, This indicates the maximum calculated resistance height of the rock arch; This represents the minimum calculated resistance height of the rock arch; Standardized evaluation indicators for support costs The calculation method is as follows: ； In the formula, This represents the cost corresponding to the minimum support stress. This represents the cost corresponding to the maximum support stress; Indicates support stress The corresponding cost.

8. A firmware chip, characterized in that, The firmware chip stores control instructions, which are embedded in the tunnel engineering analysis equipment or the geomechanical parameter acquisition terminal. When the control equipment or the geomechanical parameter acquisition terminal executes the control instructions, it completes the steps in the comprehensive determination method of the resistance height of the rock arch of the tunnel in soft and hard interactive strata as described in any one of claims 1-7.

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