Deep circular tunnel displacement analytical solution calculation method

Abstract

The invention discloses a deep circular tunnel displacement analytical solution calculation method. The method comprises the steps that tunnel area rock stratum geological parameters and rock physical and mechanical characteristics are obtained; deducing a viscoelastic-plastic creep model conforming to a rock rheological whole process behavior based on a laboratory rheological test result; a tunnel stress field under the Mohr-Coulomb failure criterion in the tunnel excavation process is calculated; deriving a displacement field function relationship of the tunnel in an elastic stress area and a plastic stress area; in combination with actual tunnel monitoring data, a deep tunnel surrounding rock deformation characteristic rule is obtained, so that the stability of the tunnel can be judged; in addition, the tunnel displacement analysis formula provided by the invention is suitable for conditions of different tunnel radiuses, different tunnel burial depths, different geological environments and the like, and the application range is wider.

Description

Technical Field

[0001] The invention relates to the technical field of civil tunnel engineering, and in particular to a method for calculating the displacement analytical solution of a deep circular tunnel. Background Art

[0002] As tunnel projects move deeper, the displacement field calculation of deep circular tunnels has become a key issue to ensure the safety of tunnel construction and operation. At present, although some achievements have been made in the research on tunnel surrounding rock deformation, the existing methods still have significant defects.

[0003] Most existing technologies do not fully consider the full process characteristics of rock rheology, and it is difficult to accurately describe the deformation behavior of surrounding rock under long-term loads. During tunnel excavation, the damage creep of surrounding rock has an important influence on the displacement field. However, existing methods rarely combine damage creep with the displacement field of deep tunnels, resulting in deviations between the calculation results and the actual situation.

[0004] In addition, the existing tunnel displacement field calculation methods have a narrow scope of application and are often limited to specific tunnel radius, burial depth and geological environment, which makes it difficult to meet the complex and changing engineering needs. At the same time, when considering the changes in surrounding rock stress caused by tunnel excavation, some methods fail to fully and accurately reflect the stress field distribution under the Mohr-Coulomb failure criterion, which in turn affects the accuracy of displacement field calculation.

[0005] The present invention aims to overcome the deficiencies of the above-mentioned prior art and provide an analytical solution method for the displacement field of deep circular tunnels that can comprehensively consider the entire rock rheology process, damage creep effect and has a wider range of applicability, thereby providing a more reliable theoretical basis for the stability assessment and design of tunnel engineering. Summary of the invention

[0006] The present invention aims to overcome the above-mentioned shortcomings of the prior art and provide a method for calculating the displacement of a deep circular tunnel by analytical solution.

[0007] The technical solution adopted by the present invention is as follows: A method for calculating the displacement of a deep circular tunnel by analytical solution, comprising the following steps: S1: Obtain geological parameters of rock formations and physical and mechanical properties of rocks in the tunnel area; S2: Derive a mechanical model that complies with the entire rock rheology process; S3: Treat the tunnel deformation problem in the infinite plane as a plane strain problem and calculate the tunnel stress field under the Mohr-Coulomb failure criterion; S4: Derive the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect; S5: Calculate the final deformation value of the tunnel surrounding rock.

[0008] Furthermore, in step S2, the plastic part of the Ramberg-Osgood classical mechanics equation is improved to obtain a new plastic model: The Ramberg-Osgood classical mechanics equation is:

[0009] Introducing the time variable t After getting :

[0010] In the formula is the total strain of the Ramberg-Osgood equation, is the elastic strain, is the plastic strain, is the plastic strain after the time variable is introduced, E is the elastic modulus, and As a material parameter, it is related to the material properties. To apply stress, is the viscosity coefficient and t is the time.

[0011] Furthermore, in step S2, the creep deformation of the rock is calculated using the following formula to form the following viscoelastic-plastic creep model:

[0012] In the formula, is the total strain of HKP model, To apply stress, is the Hooke's elastic modulus, is the Kelvin bulk elastic modulus, Kelvin volume viscosity, is the viscosity coefficient of the plastic element, and is a parameter related to material properties, is the long-term intensity and t is the time.

[0013] Furthermore, the elastic stress field of the tunnel under the Mohr-Coulomb failure criterion in step S3 is specifically calculated using the following formula:

[0014] In the formula, is the hydrostatic stress of the circular tunnel, , , are elastic radial stress, hoop stress and axial stress respectively, is the radius of the tunnel plastic zone, is the tunnel radius, , is the internal friction angle of surrounding rock, is the uniaxial compressive strength, and r is the radial distance from the tunnel center.

[0015] Furthermore, the plastic stress field of the tunnel under the Mohr-Coulomb failure criterion in step S3 is specifically calculated using the following formula:

[0016] In the formula, , , are plastic radial stress, hoop stress and axial stress respectively. is the tunnel radius, , is the internal friction angle of surrounding rock, is the uniaxial compressive strength, and r is the radial distance from the tunnel center.

[0017] Furthermore, in step S4, the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect is derived, and the following displacement analytical solution is specifically adopted: The rock creep mechanics model ( )Combined with the stress field in the elastic zone, the analytical solution for the displacement in the elastic zone of the tunnel surrounding rock is obtained:

[0018] In the formula, is the time-varying displacement solution of the elastic region of the tunnel.

[0019] Furthermore, in step S4, the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect is derived, and the following displacement analytical solution is specifically adopted: The rock creep mechanics model ( )Combined with the stress field in the plastic zone, the analytical solution of the displacement in the plastic zone of the tunnel surrounding rock is obtained:

[0020] in,

[0021]

[0022] In the formula is the plastic displacement of the tunnel, is the coefficient of expansion, is the Kelvin bulk shear modulus, is the Kelvin volume viscosity, is the viscosity coefficient of the plastic element.

[0023] Furthermore, the process of obtaining geological parameters of rock formations and physical and mechanical properties of rocks in the tunnel area includes conducting mechanical property experiments on rock samples in the tunnel area and determining relevant parameters based on creep test results.

[0024] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. Innovation of rheological model to accurately describe the whole process of rock deformation The viscoelastic-plastic creep model is constructed, integrating Hooke's body, Kelvin body and improved plastic elements, which completely covers the rheological process of rock from elastic deformation, viscoelastic deformation to viscoelastic-plastic deformation. Compared with the traditional model, this model divides the stress level into and The strain expression can more accurately describe the deformation characteristics of rocks under different stress states, solving the technical problem that traditional models cannot fully reflect the complex rheological behavior of rocks.

[0025] 2. Improve the theoretical analysis system and improve the prediction accuracy of tunnel deformation Combined with the Mohr-Coulomb failure criterion, the stress fields in the elastic and plastic zones of the tunnel are derived, and the rock rheological model is further coupled to obtain the analytical solution of the displacement fields in the elastic and plastic zones considering the time effect. This theoretical system not only quantifies the stress distribution of the surrounding rock, but also dynamically predicts the deformation of the tunnel surrounding rock over time by introducing time parameters (such as viscosity coefficient and time function), breaking through the limitations of traditional methods for long-term deformation prediction and providing a more accurate theoretical tool for tunnel deformation analysis.

[0026] 3. The engineering application value is significant, guiding the safe design and construction of tunnels Based on the model and analytical solution of this application, the deformation value of the tunnel surrounding rock can be accurately calculated, providing a quantitative basis for tunnel stability assessment. Optimize support design: Determine the strength and layout of the support structure (such as anchor length and lining thickness) through the plastic zone range and displacement distribution to avoid over-design or insufficient support; Predict risk trends: Dynamically analyze the development of surrounding rock deformation over time, provide early warning of potential unstable areas, guide construction schedule adjustments and reinforcement measures, reduce engineering safety risks, and improve the safety and economy of tunnel construction and operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The figure is a schematic diagram of the method flow of the present invention.

[0028] Figure 2 This is a simplified diagram of the rock rheology model calculation of the method of the present invention.

[0029] Figure 3 This is a diagram of the circular tunnel calculation model of the method of the present invention.

[0030] Figure 4 Comparison between the calculated value and the monitored value of the analytical solution of the method of the present invention.

[0031] Figure 5 It is the surrounding rock creep parameter of the method of the present invention. DETAILED DESCRIPTION

[0032] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0033] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0034] Embodiment 1 In this embodiment, if Figure 1-3 As shown, a method for calculating the displacement of a deep circular tunnel by analytical solution includes the following steps: S1: Obtain geological parameters of rock formations and physical and mechanical properties of rocks in the tunnel area; The geological parameters of the tunnel surrounding rock (such as lithology, burial depth, and groundwater distribution) are obtained through on-site exploration (such as drilling sampling and geophysical exploration).

[0035] The physical and mechanical parameters of rocks are determined by laboratory tests (such as uniaxial compression and triaxial creep tests), including elastic modulus, Poisson's ratio, internal friction angle, cohesion, long-term strength, creep parameters (such as , , , )wait.

[0036] The accuracy of the parameters directly affects the reliability of subsequent stress and displacement field calculations.

[0037] S2: Derive a mechanical model that complies with the entire rock rheology process; In order to establish a mechanical model that can describe the whole process of rock deformation from elastic deformation → viscoelastic deformation → viscoelastic-plastic deformation, and provide a theoretical basis for the long-term deformation prediction of surrounding rock in deep tunnels; Limitations of traditional models: The Ramberg-Osgood equation was originally used to describe nonlinear elastic and plastic deformation under monotonic loading, but the time effect was not considered.

[0038] Step S2 improves the Ramberg-Osgood equation and constructs a mechanical model of the entire rock rheology process. For the first time, the time-dependent plastic deformation is incorporated into the surrounding rock analysis of deep tunnels, providing key theoretical support for subsequent displacement field calculations and significantly improving the accuracy of long-term deformation prediction.

[0039] S3: Treat the tunnel deformation problem in the infinite plane as a plane strain problem and calculate the tunnel stress field under the Mohr-Coulomb failure criterion; The three-dimensional deformation problem of deep circular tunnel is simplified to a two-dimensional plane strain problem. The stress distribution in the elastic and plastic zones of the surrounding rock is calculated based on the Mohr-Coulomb failure criterion, which provides a basis for the subsequent displacement field analysis.

[0040] Applicable conditions: The tunnel length is much larger than the cross-sectional size, the axial deformation can be ignored, and it can be simplified to a two-dimensional problem. This method can reduce the computational complexity, facilitate the derivation of analytical solutions, and fit the actual deformation characteristics of deep tunnels (significant axial constraints).

[0041] Step S3 simplifies the complex three-dimensional tunnel deformation problem into a two-dimensional stress analysis through the plane strain assumption and the Mohr-Coulomb criterion, providing key input for the subsequent displacement field calculation and being the core link of the long-term stability assessment of deep tunnels.

[0042] S4: Derive the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect; Combining the viscoelastic-plastic creep model of rock with the Mohr-Coulomb stress field, the analytical solution of the displacements in the elastic and plastic zones of the tunnel surrounding rock considering the time effect is derived to predict the long-term deformation of deep tunnels.

[0043] Quantification of time effect: The time parameter is introduced into the displacement solution through the viscoelastic-plastic model to achieve dynamic prediction of long-term deformation.

[0044] Covering the whole process: displacement in the elastic zone reflects viscoelastic deformation, and displacement in the plastic zone reflects viscoelastic-plastic deformation, fitting the whole process from elasticity to destruction of rock.

[0045] Engineering applicability: The analytical solution is concise and the parameters can be obtained through experiments, which is suitable for tunnel projects under different geological conditions.

[0046] Step S4 combines the viscoelastic-plastic model with the stress field to derive a displacement analytical solution that takes into account the time effect, breaking through the limitation of traditional methods that only focus on instantaneous deformation and providing a key theoretical tool for long-term stability analysis of deep tunnels. Its innovation lies in the explicit expression of the time-displacement relationship and the coupling of the deformation mechanism of the whole process, which significantly improves the reliability of engineering prediction.

[0047] S5: Calculate the final deformation value of the tunnel surrounding rock.

[0048] By combining the information obtained in the previous steps, the deformation values ​​of the tunnel surrounding rock at different positions and times are calculated, providing a quantitative basis for evaluating the stability of the tunnel and guiding the design, construction and maintenance decisions of the tunnel project.

[0049] Stability assessment: The stability of the tunnel can be determined based on the calculated surrounding rock deformation values. For example, if the displacement value of a certain area around the tunnel exceeds the design allowable deformation range, it means that the surrounding rock in this area may be at risk of instability and support measures need to be strengthened.

[0050] Support design optimization: By comparing the deformation values ​​at different locations, determine the areas that need key support and rationally design the strength and stiffness of the support structure. For areas with large deformation, increase the length of the anchor rod, increase the lining thickness, or use stronger support materials.

[0051] Construction decision guidance: During the tunnel construction process, the construction progress and construction methods are determined based on the real-time calculated surrounding rock deformation values. If the deformation increases too quickly, construction may need to be suspended and reinforcement measures taken before continuing.

[0052] Long-term monitoring and maintenance: Provide benchmark data for long-term monitoring and maintenance of tunnels. During the operation phase, regularly monitor surrounding rock deformation and compare it with the calculation results to promptly detect abnormal deformation, perform necessary maintenance and repair work, and ensure the safe use of the tunnel.

[0053] Furthermore, in step S2, the plastic part of the Ramberg-Osgood classical mechanics equation is improved to obtain a new plastic model: The Ramberg-Osgood classical mechanics equation is:

[0054] Introducing the time variable t After getting :

[0055] In the formula is the total strain of the Ramberg-Osgood equation, is the elastic strain, is the plastic strain, is the plastic strain after the time variable is introduced, E is the elastic modulus, and As a material parameter, it is related to the material properties. To apply stress, is the viscosity coefficient, and t is the time. This formula represents the total strain It consists of two parts, Represents the elastic strain part, which is composed of the elastic modulus E and stress Determination, reflecting the elastic deformation of the material at the moment of force; is the plastic deformation term, but time has not been introduced at this time. It is just a prelude to the subsequent combination of time. k and n are parameters related to material properties, which partially reflect the nonlinear relationship between stress and strain in the plastic stage of the material. Compared with the traditional elastic model, this formula can better describe the complex deformation characteristics of the material in the plastic stage.

[0056]

[0057] This formula introduces time t and the viscosity coefficient of the plastic element based on the above plastic strain . k and n are still material parameters. is stress. This formula describes the change of plastic strain over time, that is, as time goes by, plastic strain will increase in the form of a power function. In tunnel engineering, the surrounding rock is subjected to stress for a long time. This formula can more realistically reflect the accumulation of plastic deformation of the surrounding rock over time. Compared with the plastic model that does not consider the time factor, it can more accurately predict the deformation trend of the surrounding rock.

[0058] The improved plastic model comprehensively considers elastic strain, plastic strain and the influence of time on plastic strain, and can more comprehensively describe the deformation behavior of rock under complex stress conditions. In deep tunnel engineering, the surrounding rock is subjected to long-term stress, and the rock will go through elastic and plastic deformation stages, and the plastic deformation will continue to develop over time. This model can simulate this process well and provide a more reliable theoretical basis for analyzing the stability of tunnel surrounding rock.

[0059] By introducing the time-dependent plastic strain formula, it has significant advantages in predicting the long-term deformation of tunnel surrounding rock. The traditional model cannot accurately reflect the change of plastic strain over time, while the improved model can take into account the time factor, making the prediction of tunnel surrounding rock deformation more in line with the actual situation, thereby providing more accurate data support for tunnel support design, construction plan formulation, etc., and reducing engineering risks.

[0060] Furthermore, in step S2, the creep deformation of the rock is calculated using the following formula to form the following viscoelastic-plastic creep model:

[0061] The above formula represents the instantaneous elastic deformation of rock. When , the Hooke body (ideal elastic element) immediately produces a strain proportional to the stress. It is the elastic modulus of the Hooke body, which reflects the ability of rock to resist elastic deformation. The strain is completely recovered after the stress is removed.

[0062]

[0063] The above equation represents the viscoelastic deformation (delayed elastic deformation) of rock. and Kelvin volume viscosity Parallel composition.

[0064]

[0065]

[0066] when (Stress is less than long-term strength): The rock undergoes only elastic (Hooke's body) and viscoelastic (Kelvin body) deformations, without plastic deformation, which is suitable for the description of the stable creep stage.

[0067] when (Stress greater than or equal to long-term strength): New is the improved time-dependent plastic strain, k and n reflect the plastic properties of the material, is the viscosity coefficient of the plastic element. This formula describes the deformation of rock entering the accelerated creep stage, reflecting the power law growth of plastic deformation with time after the stress exceeds the long-term strength.

[0068] In the formula, is the total strain of HKP model, To apply stress, is the Hooke's elastic modulus, is the Kelvin bulk elastic modulus, Kelvin volume viscosity, is the viscosity coefficient of the plastic element, and is a parameter related to material properties, is the long-term intensity and t is the time.

[0069] The model completely covers the entire rheological process of rock from elasticity, viscoelasticity to viscoelastic plasticity through the expression of stress levels. It is suitable for long-term deformation analysis of surrounding rock of deep tunnels, provides a theoretical basis for predicting stability and designing support structures, and solves the problem that traditional models cannot fully describe the complex rheological behavior of rock.

[0070] Furthermore, the elastic stress field of the tunnel under the Mohr-Coulomb failure criterion in step S3 is specifically calculated using the following formula:

[0071] Describe the distribution of radial stress with radial distance r in the elastic zone of the tunnel.

[0072] is the initial hydrostatic stress, which is the uniform stress on the surrounding rock before excavation; Reflecting stress redistribution, as r increases, this term decreases, and the radial stress approaches ; , reflecting the internal friction angle of the surrounding rock The impact on stress distribution is that the larger the internal friction angle and the larger the N value, the more significant the stress redistribution.

[0073]

[0074] Characterizes the distribution of hoop stress in the elastic zone. The hoop stress around the tunnel is r= The maximum is , and it gradually decreases with the increase of r, which reflects the phenomenon of circumferential stress concentration after tunnel excavation. Compared with the radial stress formula, the difference between the two reflects the shear stress state in the elastic zone, which is one of the bases for judging whether the surrounding rock has entered plasticity.

[0075]

[0076] Under the plane strain assumption, the axial stress does not vary with radial distance and is always equal to the initial hydrostatic stress , simplifying the three-dimensional problem into a two-dimensional analysis.

[0077]

[0078] Determine the scope of the plastic zone of the tunnel surrounding rock.

[0079] is the tunnel radius, and the formula integrates the initial stress , surrounding rock strength ( , ) Increase or Decrease (the strength of the surrounding rock decreases), The increase of pressure, expansion of plastic zone and decrease of surrounding rock stability are the key parameters of support design.

[0080] In the formula, is the hydrostatic stress of the circular tunnel, , , are elastic radial stress, hoop stress and axial stress respectively, is the radius of the tunnel plastic zone, is the tunnel radius, , is the internal friction angle of surrounding rock, is the uniaxial compressive strength, and r is the radial distance from the tunnel center.

[0081] Furthermore, the plastic stress field of the tunnel under the Mohr-Coulomb failure criterion in step S3 is specifically calculated using the following formula:

[0082] The formula describes the distribution of radial stress in the plastic zone with radial distance r. It is the uniaxial compressive strength of rock, reflecting the inherent strength of the material; ( is the internal friction angle of surrounding rock), reflecting the influence of rock shear properties on stress. The term reflects the attenuation law of stress with distance: the farther away from the tunnel center (the larger r is), the radial stress gradually increases and approaches the stress state in the elastic zone.

[0083]

[0084] Hoop stress is a key indicator of plastic deformation of tunnel surrounding rock. Compared with the radial stress formula, The item amplifies the hoop stress level, reflecting the hoop stress concentration characteristics after tunnel excavation. Reflecting the stress distribution, the closer to the tunnel (the smaller r), the greater the circumferential stress, which is more likely to cause shear failure of the surrounding rock.

[0085]

[0086] Based on the plane strain assumption, the axial stress is taken as the average value of the radial and hoop stresses, and the three-dimensional stress state is simplified to a two-dimensional analysis. This method is suitable for engineering scenarios where the tunnel length is much larger than the cross-section, reflecting the uniformity of the axial stress in the plastic zone.

[0087] In the formula, , , are plastic radial stress, hoop stress and axial stress respectively. is the tunnel radius, , is the internal friction angle of surrounding rock, is the uniaxial compressive strength, and r is the radial distance from the tunnel center.

[0088] These formulas are based on the Mohr-Coulomb failure criterion and combined with the theory of elastic mechanics to quantify the stress distribution in the elastic zone and the range of the plastic zone of the tunnel, providing a theoretical basis for analyzing the stability of the surrounding rock and designing the support structure (such as determining the length of the anchor rod and the thickness of the lining), and reflecting the mechanical relationship between the stress, strength and deformation of the surrounding rock. In engineering applications, the range of surrounding rock failure can be determined by analyzing the stress field in the plastic zone, providing a theoretical basis for the design of the support structure (such as determining the anchor depth of the anchor rod and the bearing capacity of the lining), and ensuring the stability of the tunnel during the plastic deformation stage.

[0089] Furthermore, in step S4, the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect is derived, and the following displacement analytical solution is specifically adopted: The rock creep mechanics model ( )Combined with the stress field in the elastic zone, the analytical solution for the displacement in the elastic zone of the tunnel surrounding rock is obtained:

[0090] In the formula, is the time-varying displacement solution of the elastic region of the tunnel.

[0091] Instantaneous elastic displacement:

[0092] The contribution of the Hooke body reflects the elastic deformation immediately generated by the stress, and It is inversely proportional to the displacement (the stiffer the material, the smaller the displacement), and decays as the radial distance r increases.

[0093] Viscoelastic displacement:

[0094] The delayed deformation dominated by Kelvin body increases with time t, and the initial deformation rate is fast (due to control), and eventually approaches a stable value , reflecting the time dependence of viscoelasticity.

[0095] Comprehensive coefficient:

[0096] Integrating the stress field characteristics and quantifying the synergistic effects of initial stress, rock strength and internal friction angle on displacement is the mathematical expression of stress redistribution in the elastic zone.

[0097] Dynamic deformation prediction: By inputting different time t, the displacement development of surrounding rock in elastic zone can be calculated, which provides theoretical reference for long-term deformation monitoring of tunnel and assists in judging the timeliness of support structure. Stability assessment basis: By analyzing the displacement distribution in elastic zone through displacement solution, if the displacement of key positions (such as around the tunnel) exceeds the limit, it indicates that surrounding rock may develop into plastic deformation, and it is necessary to optimize support measures (such as increasing anchor density) in time to ensure the safety of tunnel structure.

[0098] Furthermore, in step S4, the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect is derived, and the following displacement analytical solution is specifically adopted: The rock creep mechanics model ( )Combined with the stress field in the plastic zone, the analytical solution of the displacement in the plastic zone of the tunnel surrounding rock is obtained:

[0099] in,

[0100]

[0101] In the formula is the plastic displacement of the tunnel, is the coefficient of expansion, is the Kelvin bulk shear modulus, is the Kelvin volume viscosity, is the viscosity coefficient of the plastic element.

[0102] It is a time function, reflecting the development of plastic displacement over time (such as creep accumulation).

[0103] The coefficient integrates rock strength, expansion characteristics and shear parameters. It reflects the distribution law of displacement with radial distance r. The closer to the tunnel (the smaller r is), the more significantly the plastic displacement is affected by stress redistribution.

[0104] Deformation mechanism coupling: and Expansion coefficient The coupling effect with the shear parameter N quantifies the composite mechanism of shear deformation and volume expansion in plastic deformation, making the formula more consistent with the real deformation behavior of rock.

[0105] Elastic-plastic boundary coordination term: , which is achieved by introducing the boundary displacement of the elastic zone , and combined with the geometric factor , ensuring that the elastic zone and the plastic zone are at the junction (r = This design reflects the integrity of surrounding rock deformation, that is, the deformation of the elastic zone will be transferred to the plastic zone through the boundary conditions, affecting the displacement distribution in the plastic zone.

[0106] Long-term deformation prediction: By inputting parameters such as time t and radial distance r, the displacement at any position in the plastic zone can be accurately calculated, and the long-term deformation trend of the tunnel surrounding rock can be dynamically predicted. For example, during the tunnel operation stage, the displacement of the plastic zone at different times can be predicted based on this formula to determine whether the stability of the surrounding rock deteriorates over time, providing a basis for maintenance decisions. Support optimization design: By analyzing the displacement distribution in the plastic zone, areas with concentrated displacement or excessive deformation can be located. For these key areas, targeted support measures (such as increasing anchor rod density and enhancing lining strength) are guided to be taken in the project to avoid tunnel structure damage caused by excessive plastic deformation and ensure project safety. Support for deformation mechanism research: The formula clearly shows the influence mechanism of time, material properties (strength, expansion, shear resistance), and stress state on plastic displacement. In scientific research, this formula can be used to carry out parameter sensitivity analysis, deeply explore the nature of rock viscoelastic-plastic deformation, and promote the development of tunnel engineering theory.

[0107] Embodiment 2 The process of obtaining the geological parameters of the rock formations and the physical and mechanical properties of the rocks in the tunnel area includes conducting mechanical property experiments on rock samples in the tunnel area and determining relevant parameters based on the creep test results.

[0108] 1. Rock sample mechanical property experiment: obtain basic mechanical parameters of rock, such as uniaxial compressive strength, elastic modulus, Poisson's ratio, internal friction angle, cohesion, etc. Implementation: Through uniaxial compression experiment, measure the uniaxial compressive strength and elastic modulus of rock; use triaxial compression experiment to analyze the shear characteristics of rock under different confining pressures, determine the internal friction angle and cohesion; carry out deformation experiment to distinguish the elastic and plastic deformation characteristics of rock, and provide basic data for mechanical model.

[0109] 2. Determine rheological parameters based on creep experiments Objective: Obtain rock rheological model parameters (such as viscosity coefficient, material constant, etc.). Implementation: Apply constant stress to the rock sample, monitor the change of strain over time, and obtain the creep curve; analyze the creep curve (initial, stable, and accelerated stages), fit the Kelvin body parameters and plastic element parameters, and support the construction of the rock rheological model.

[0110] Through two types of experiments, static mechanical parameters and dynamic rheological parameters are comprehensively acquired, providing accurate data for subsequent tunnel stress field analysis, displacement field derivation and deformation calculation, thus ensuring the reliability of tunnel stability assessment and support design.

[0111] Embodiment 3 The cross section of a tunnel is circular, the radius of the tunnel is 5m, the terrain in the study area is undulating, and the maximum burial depth of the tunnel is 200m. During the construction process, the tunnel is monitored for arch settlement and peripheral convergence (A and B).

[0112] Through the mechanical property experiment of the rock samples in the tunnel area, based on the creep test results, the following results were obtained: Figure 5 Creep parameters of surrounding rock shown; According to the geometric structure of the tunnel, combined with the creep parameters of the surrounding rock, they are substituted into the displacement solution function relationship in the present invention to obtain the final calculated displacement value of the tunnel surrounding rock.

[0113] like Figure 4 As shown, by comparing the calculated value with the monitored value, the feasibility and applicability of the calculated value can be verified.

[0114] The above description is only a preferred embodiment of the invention and is not intended to limit the invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the invention should be included in the protection scope of the invention.

Claims

1. A method for calculating the displacement of a deep circular tunnel by analytical solution, characterized in that: The following steps are involved: S1: Obtain geological parameters of rock formations and physical and mechanical properties of rocks in the tunnel area; S2: Derive a mechanical model that complies with the entire rock rheology process; S3: Treat the tunnel deformation problem in the infinite plane as a plane strain problem and calculate the tunnel stress field under the Mohr-Coulomb failure criterion; S4: Derive the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect; S5: Calculate the final deformation value of the tunnel surrounding rock.

2. According to the method for calculating the displacement of a deep circular tunnel according to claim 1, it is characterized by: In step S2, the plastic part of the Ramberg-Osgood classical mechanics equation is improved to obtain a new plastic model: The Ramberg-Osgood classical mechanics equation is: Introducing the time variable t After getting : In the formula is the total strain of the Ramberg-Osgood equation, is the elastic strain, is the plastic strain, is the plastic strain after the time variable is introduced, E is the elastic modulus, and As a material parameter, it is related to the material properties. To apply stress, is the viscosity coefficient and t is the time.

3. According to the method for calculating the displacement of a deep circular tunnel according to claim 2, it is characterized by: In step S2, the creep deformation of the rock is calculated using the following formula to form the following viscoelastic-plastic creep model: In the formula, is the total strain of HKP model, To apply stress, is the Hooke's elastic modulus, is the Kelvin bulk elastic modulus, Kelvin volume viscosity, is the viscosity coefficient of the plastic element, and is a parameter related to material properties, is the long-term intensity and t is the time.

4. According to the method for calculating the displacement of a deep circular tunnel according to claim 3, it is characterized by: The elastic stress field of the tunnel under the Mohr-Coulomb failure criterion in step S3 is specifically calculated using the following formula: In the formula, is the hydrostatic stress of the circular tunnel, , , are elastic radial stress, hoop stress and axial stress respectively, is the radius of the tunnel plastic zone, is the tunnel radius, , is the internal friction angle of surrounding rock, is the uniaxial compressive strength, and r is the radial distance from the tunnel center.

5. According to the method for calculating the displacement of a deep circular tunnel according to claim 4, it is characterized by: The plastic stress field of the tunnel under the Mohr-Coulomb failure criterion in step S3 is specifically calculated using the following formula: In the formula, , , are plastic radial stress, hoop stress and axial stress respectively, is the tunnel radius, , is the internal friction angle of surrounding rock, is the uniaxial compressive strength, and r is the radial distance from the tunnel center.

6. A method for calculating displacement of a deep circular tunnel according to claim 5, characterized in that: In step S4, the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect is derived, and the following displacement analytical solution is specifically adopted: The rock creep mechanics model ( )Combined with the stress field in the elastic zone, the analytical solution for the displacement in the elastic zone of the tunnel surrounding rock is obtained: In the formula, is the time-varying displacement solution of the elastic region of the tunnel.

7. A method for calculating displacement of a deep circular tunnel according to claim 6, characterized in that: In step S4, the functional relationship between the displacement field in the elastic zone and the displacement field in the plastic zone of the tunnel under the time effect is derived, and the following displacement analytical solution is specifically adopted: The rock creep mechanics model ( )Combined with the stress field in the plastic zone, the analytical solution of the displacement in the plastic zone of the tunnel surrounding rock is obtained: in, In the formula is the plastic displacement of the tunnel, is the expansion coefficient, is the Hooke body shear modulus, is the Kelvin bulk shear modulus, is the Kelvin volume viscosity, is the viscosity coefficient of the plastic element.

8. The method for calculating the displacement of a deep circular tunnel according to claim 1, characterized in that: The process of obtaining the geological parameters of the rock formations in the tunnel area and the physical and mechanical properties of the rocks includes conducting mechanical property experiments on rock samples in the tunnel area and determining relevant parameters based on creep test results.

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