Tunnel deformation pressure calculation method and device

Abstract

The invention relates to the technical field of engineering, in particular to a tunnel deformation pressure calculation method and device. Comprising the following steps: S1, acquiring basic parameters of tunnel engineering, including tunnel burial depth, surrounding rock level and tunnel span; s2, according to the construction design, a preliminary bracing scheme of the tunnel is determined, the preliminary bracing scheme comprises sprayed concrete parameters and steel frame parameters, and the flexural rigidity of a preliminary bracing section is calculated; s3, based on the deformation pressure sample data, establishing a relation model between the deformation pressure and the surrounding rock level, the tunnel span and the initial support section flexural rigidity by adopting a multivariate nonlinear regression analysis method; s4, calculating the vertical deformation pressure of the tunnel supporting structure according to the relation model and the basic parameters, and calculating the horizontal deformation pressure; and S5, outputting the vertical deformation pressure and the horizontal deformation pressure. According to the method, the deformation pressure is calculated based on the basic parameters, accurate calculation of the stress state of the tunnel support is achieved according to multi-factor regression analysis and consideration of the support rigidity, and the design is more economical, reasonable, safe and reliable.

Description

Technical Field

[0001] This invention relates to the field of engineering technology, and in particular to a method and apparatus for calculating tunnel deformation pressure. Background Technology

[0002] Currently, the design of support structures for deep-buried railway tunnels in China mainly adopts the rock pressure calculation method for deep-buried tunnels in the "Code for Design of Railway Tunnels" (TB10003) (hereinafter referred to as the "Tunnel Code"). This method is a semi-empirical formula for loosening pressure established in the 1980s based on statistical data from the collapse of over 1,000 small-span tunnels. The expression is simple, the physical concepts are clear, and it is easy for engineering technicians to use. With the continuous improvement of tunnel construction technology in China, tunnel construction methods have gradually transitioned from the era of traditional manual labor and small machinery to large-scale mechanized construction. In terms of construction philosophy, the focus is on protecting the surrounding rock and minimizing disturbance to it, so as to fully utilize the self-supporting capacity of the surrounding rock. Tunnel support has gradually shifted from passive support to active support. The main load borne by the tunnel support structure is no longer loosening pressure, but has been transformed into deformation pressure. Using the loosening pressure calculation method in the "Tunnel Code" for the design of tunnel support structures is inconsistent with the actual site conditions. Therefore, considering the current level of tunnel construction technology in China and adapting to the needs of high-quality development in tunnel construction technology, it is necessary to use deformation pressure gauges to guide tunnel construction.

[0003] Currently, the methods for calculating surrounding rock pressure can be categorized into theoretical calculation methods, numerical simulation methods, and statistical regression methods. Internationally, the main theoretical calculation methods include the Fenner and Kastner formulas. These methods are based on elastoplastic mechanics and the Mohr-Coulomb yield criterion, primarily considering two influencing factors: surrounding rock parameters and tunnel span. They assume that the deformation pressure of the surrounding rock is the weight of the rock mass within the plastic zone, and the calculated pressure often does not match the actual field conditions. The Protodyakonov formula is a method for calculating loosening pressure. This method assumes the existence of a collapse arch in deeply buried tunnels, and that the loosening pressure is related to the tunnel span, height, and surrounding rock parameters. Domestically, Zeng Qianbang et al. based their methods on the generalized Hoe... The k-Brown yield criterion has been used to derive a method for calculating the plastic deformation pressure of ideal elastoplastic surrounding rock in deeply buried circular tunnels. Other scholars have also conducted in-depth research on the elastoplastic stress field and displacement of brittle and strain-softened surrounding rock using different rock mass constitutive relations and strength criteria, but the results have not been further applied and promoted. Numerical simulation mainly involves establishing a numerical model to simulate the dynamic evolution of the surrounding rock state after tunnel excavation and analyzing the deformation pressure between the surrounding rock and the initial support. A representative method in China is the deformation pressure calculation method based on the pressure arch, which assumes that after tunnel excavation... The surrounding rock will form a pressure arch, and the force acting on the support structure is the weight of the rock mass inside the pressure arch. The surrounding rock pressure of this method is related to factors such as burial depth, unit weight of surrounding rock, surrounding rock parameters, and span. Due to its complex operation and the large number of factors to consider, this method has not been further promoted and used. The statistical regression method establishes a method for calculating the surrounding rock load by performing statistical regression analysis on field test data. Representative methods abroad mainly include surrounding rock pressure calculation methods based on Q system, RMR, and GSI. These methods mainly consider the influence of surrounding rock properties, tunnel span, and burial depth on surrounding rock pressure. However, due to the limited international application of this method, it has not been widely adopted. The theories and methods for constructing internal and external tunnels are different, so these three methods are not applicable in China. Domestic researchers such as Wu Dong and Liu Xuezeng have analyzed the field-measured deformation pressure data and studied its influencing factors. The relevant research results have certain reference value for engineering construction, but no quantitative method for calculating deformation pressure has been given to guide actual engineering. Wang Mingnian of Southwest Jiaotong University, based on a large amount of field monitoring data of deformation pressure in China, mainly considered two factors: surrounding rock grade and tunnel span. He derived and established a method for calculating the deformation pressure of deep-buried tunnels through multivariate nonlinear regression analysis.

[0004] In summary, existing technologies cannot accurately reflect the effect of support structure stiffness on deformation pressure, leading to conservative support designs and uneconomical structural dimensions. To address this issue, it is necessary to propose a new method for calculating deformation pressure that fully considers support stiffness during the calculation process, making the support structure design more in line with the needs of modern tunnel construction. Summary of the Invention

[0005] This application aims to address the problem that existing methods for calculating tunnel surrounding rock pressure do not consider the stiffness of the support structure, leading to inconsistencies between calculated and actual results. This application provides a method for calculating tunnel deformation pressure, which can accurately calculate deformation pressure based on the surrounding rock grade, tunnel span, and support structure stiffness, making support structure design more economical and rational. In tunnel support design, the deformation pressure calculation method obtained from multi-factor regression analysis can accurately predict the stress state of the tunnel support by considering the influence of support stiffness on the stress, thereby improving the safety and reliability of the design.

[0006] In a first aspect, embodiments of this application provide a method for calculating tunnel deformation pressure, which may include: S1. Obtain basic parameters for tunnel engineering, including tunnel depth, surrounding rock grade, and tunnel span; S2. Determine the initial support scheme for the tunnel based on the construction design. The initial support scheme includes shotcrete parameters and steel frame parameters, and calculate the bending stiffness of the initial support section. S3. Based on the deformation pressure sample data, a multivariate nonlinear regression analysis method is used to establish a relationship model between deformation pressure and surrounding rock grade, tunnel span and bending stiffness of initial support section; S4. Calculate the vertical deformation pressure of the tunnel support structure based on the relationship model and the basic parameters, and calculate the horizontal deformation pressure based on the vertical deformation pressure; S5. Output the vertical deformation pressure and horizontal deformation pressure.

[0007] The tunnel deformation pressure calculation method according to the embodiments of this application has at least the following beneficial effects: The tunnel deformation pressure calculation method of this application first obtains basic parameters such as tunnel burial depth, surrounding rock grade, and span to provide necessary input for subsequent modeling. Then, combined with the construction design, it extracts parameters of shotcrete and steel frame to calculate the bending stiffness of the initial support section. Next, based on a large amount of field monitoring data, it establishes a prediction model for vertical deformation pressure through multivariate nonlinear regression. Finally, based on the established relationship model, it calculates and outputs the deformation pressure value of the target tunnel, providing a quantitative basis for support structure design. In particular, by introducing support stiffness as a key factor and modeling it together with surrounding rock grade and tunnel span, the engineering applicability and accuracy of deformation pressure prediction are significantly improved, realizing the optimization and upgrade of support design from "experience-based judgment" to "data-driven".

[0008] According to some embodiments of this application, the calculation of the initial support section bending stiffness in step S2 includes: determining the elastic modulus and thickness of the shotcrete, as well as the elastic modulus, cross-sectional area and spacing of the steel frame, and obtaining the initial support section bending stiffness based on the combination relationship between the shotcrete and the steel frame.

[0009] According to some embodiments of this application, the relationship model described in step S3 is determined by performing single-factor regression fitting on sample data of surrounding rock grade, tunnel span and initial support section bending stiffness, and then performing multi-factor nonlinear regression analysis.

[0010] According to some embodiments of this application, the single-factor regression fitting includes: Based on field monitoring data, single-factor nonlinear regression analysis was conducted on the relationships between the surrounding rock grade and deformation pressure, the tunnel span and deformation pressure, and the bending stiffness of the initial support section and deformation pressure.

[0011] According to some embodiments of this application, the formula for calculating the vertical deformation pressure is as follows: q =3.62 e 0.56S · ω ·2 0.24k in, q This represents the vertical deformation pressure, e is the natural constant, and S represents the surrounding rock grade. ω denoted by the span correction factor, and k represents the flexural stiffness of the initial support section composed of shotcrete and steel frame.

[0012] According to some embodiments of this application, the method further includes performing a goodness-of-fit check on the relational model and adjusting the coefficients of the relational model based on the check result.

[0013] Secondly, embodiments of this application provide a tunnel deformation pressure calculation device, which may include: The parameter acquisition module is used to acquire basic parameters of tunnel engineering, including tunnel depth, surrounding rock grade, and tunnel span. The support scheme module is used to determine the initial support scheme for the tunnel based on the construction design and to calculate the bending stiffness of the initial support section. The regression analysis module is used to establish a model of the relationship between deformation pressure and surrounding rock grade, tunnel span and bending stiffness of initial support section based on deformation pressure sample data and multivariate nonlinear regression analysis method. The pressure calculation module is used to calculate the vertical deformation pressure of the tunnel support structure based on the relationship model and the basic parameters, and to calculate the horizontal deformation pressure based on the vertical deformation pressure. The result output module is used to output the vertical deformation pressure and the horizontal deformation pressure.

[0014] The tunnel deformation pressure calculation device according to the embodiments of this application has at least the following beneficial effects: The tunnel deformation pressure calculation device of this application embodiment first collects basic data such as tunnel burial depth, surrounding rock grade, and span through a parameter acquisition module; then, it calculates the initial support section bending stiffness through a support scheme module combined with construction design parameters; subsequently, a regression analysis module establishes a predictive model of vertical deformation pressure using field monitoring sample data; finally, the pressure calculation module calculates the deformation pressure based on the established model and outputs the results through a result output module. The modular design automates data acquisition, stiffness calculation, modeling, calculation, and result output, improving the efficiency and accuracy of vertical deformation pressure calculation and realizing the scientific and intelligent design of tunnel support.

[0015] According to some embodiments of this application, the parameter acquisition module is further configured to receive monitoring data from field sensors and preprocess the data, including noise reduction and outlier filtering.

[0016] According to some embodiments of this application, the regression analysis module includes a single-factor analysis submodule and a multi-factor fitting submodule. The single-factor analysis submodule is used to fit the individual effects of surrounding rock grade, tunnel span, and initial support section bending resistance on deformation pressure, respectively. The multi-factor fitting submodule is used to perform multivariate nonlinear regression based on the results of the single-factor analysis.

[0017] According to some embodiments of this application, the pressure calculation module includes a model optimization unit for dynamically adjusting the coefficients of the relationship model based on the goodness of fit.

[0018] Other features and advantages of this application will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing this application. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the surrounding rock characteristic curve of Embodiment 1 of this application; Figure 2 This is a flowchart illustrating the steps of a tunnel deformation pressure calculation method according to Embodiment 1 of this application; Figure 3 The regression curve of deformation pressure versus surrounding rock grade in Example 3 of this application; Figure 4 The regression curve (linear function) of deformation pressure versus tunnel span in Embodiment 3 of this application is shown. Figure 5 The regression curve (power function) of deformation pressure versus tunnel span in Embodiment 3 of this application is shown. Figure 6 The regression curve (linear function) of the deformation pressure and the bending stiffness of the initial support section in Embodiment 3 of this application is shown. Figure 7The regression curve (logarithmic function) of deformation pressure and bending stiffness of the initial support section in Embodiment 3 of this application is shown. Figure 8 The comparison curves show the calculation results of two methods for different surrounding rock grades at a speed of 350 km / h in Example 3 of this application. Figure 9 This is a comparison curve of the calculation results of two methods for different surrounding rock grades at a speed of 250km / h in Example 3 of this application. Detailed Implementation

[0020] The present application will now be described in further detail with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the subject matter of the present application to the following embodiments. All technologies implemented based on the content of the present application fall within the scope of protection of the present application.

[0021] Unless otherwise specified, the terms "upper," "lower," "left," "right," "center," "inner," "outer," and "side" used in the description of specific embodiments of this application to indicate orientation or positional relationships are based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the solution in this application or simplifying the description in specific embodiments, so as to enable those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on this application.

[0022] In the description of the embodiments of this application, technical terms such as "first" and "second" only distinguish one entity or operation from another, and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary or secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] Example 1 During the research on the stress of tunnel support structures, the applicant found that existing methods for calculating tunnel surrounding rock pressure are mainly based on elastoplastic theory and the Mohr-Coulomb yield criterion.

[0025] Based on the elastoplastic theory and the Mohr-Coulomb yield criterion, the relationship between tunnel support force P and tunnel surrounding rock deformation can be established, as shown in formula (1). According to this formula, the characteristic curve of the surrounding rock can be plotted, as shown in formula (1). Figure 1 As shown.

[0026]

[0027] In the formula: P is the support force inside the tunnel. c , φ These represent the cohesion and friction angle of the surrounding rock, respectively. σ y The value is the magnitude of the in-situ stress, and 'a' is the tunnel radius. u For the displacement around the tunnel, K = E / 2(1 + μ) , E and μ These represent the elastic modulus and Poisson's ratio, respectively.

[0028] Please refer to Figure 1 , Figure 1 This is a schematic diagram of the characteristic curve of the surrounding rock. After tunnel excavation, stress redistribution occurs. As the surrounding rock deforms, it gradually evolves from an elastic state to an elasto-plastic state. If the surrounding rock is not supported and its deformation is not controlled at this point, the cracks will further develop, leading to rock loosening and collapse, thus generating a collapse load. Figure 1 As shown by the red dashed line, if effective support is implemented to control the deformation of the surrounding rock before the tunnel enters a relaxed state, the support structure mainly bears the deformation pressure. Support structures with different stiffnesses bear different magnitudes of deformation pressure, and the displacement achieved when the surrounding rock reaches equilibrium also differs. For example... Figure 1 As shown, the stiffness of support structure 1 K 1 =P 1 / (u 1 -u 0 ) stiffness of support structure 2 K 2 =P 2 / (u 2 -u 0 ) Although the two support structures were constructed at the same time, due to K 1 >K 2, therefore P 1 >P 2, u 1 <u2. In other words, the greater the support stiffness, the greater the deformation pressure borne by the support and the smaller the surrounding rock displacement. Therefore, the deformation pressure borne by the support structure is directly related to its stiffness, but current methods for calculating deformation pressure do not consider support stiffness. To accurately assess the deformation pressure borne by the support structure in deep-buried tunnel design, complex theoretical calculations or numerical simulations are required, yielding only approximate results based on loosening pressure, which cannot directly reflect the influence of support structure stiffness on surrounding rock pressure. In solving practical engineering problems, existing calculation methods cannot meet design requirements to achieve a more economical and rational support structure design.

[0029] Therefore, after studying a large amount of field monitoring data on deformation pressure and support stiffness parameters, the applicant proposed a method for calculating tunnel deformation pressure. This method takes into account the stiffness of the support structure and establishes a deformation pressure calculation model based on the surrounding rock grade, tunnel span and support stiffness through a multi-factor nonlinear regression analysis technique. This enables a more accurate prediction of the stress state of the support structure, making the tunnel support design results more realistic, economical and reliable.

[0030] Please refer to Figure 2 , Figure 2 This diagram illustrates the steps of a method for calculating tunnel deformation pressure according to an embodiment of this application. The method may include: S1. Obtain basic parameters for tunnel engineering, including tunnel depth, surrounding rock grade, and tunnel span; S2. Determine the initial support scheme for the tunnel based on the construction design. The initial support scheme includes shotcrete parameters and steel frame parameters, and calculate the bending stiffness of the initial support section. S3. Based on the deformation pressure sample data, a multivariate nonlinear regression analysis method is used to establish a relationship model between deformation pressure and surrounding rock grade, tunnel span and bending stiffness of initial support section; S4. Calculate the vertical deformation pressure of the tunnel support structure based on the relationship model and the basic parameters, and calculate the horizontal deformation pressure based on the vertical deformation pressure; S5. Output the vertical deformation pressure and horizontal deformation pressure.

[0031] The tunnel deformation pressure calculation method according to the embodiments of this application has at least the following beneficial effects: The tunnel deformation pressure calculation method of this application first obtains basic parameters such as tunnel burial depth, surrounding rock grade, and span to provide necessary input for subsequent modeling. Then, combined with the construction design, it extracts parameters of shotcrete and steel frame to calculate the bending stiffness of the initial support section. Next, based on a large amount of field monitoring data, it establishes a prediction model for vertical deformation pressure through multivariate nonlinear regression. Finally, based on the established relationship model, it calculates and outputs the deformation pressure value of the target tunnel, providing a quantitative basis for support structure design. In particular, by introducing support stiffness as a key factor and modeling it together with surrounding rock grade and tunnel span, the engineering applicability and accuracy of deformation pressure prediction are significantly improved, realizing the optimization and upgrade of support design from "experience-based judgment" to "data-driven".

[0032] According to some embodiments of this application, the calculation of the initial support section bending stiffness in step S2 includes: determining the elastic modulus and thickness of the shotcrete, as well as the elastic modulus, cross-sectional area and spacing of the steel frame, and obtaining the initial support section bending stiffness based on the combination relationship between the shotcrete and the steel frame.

[0033] According to some embodiments of this application, the relationship model described in step S3 is determined by performing single-factor regression fitting on sample data of surrounding rock grade, tunnel span and initial support section bending stiffness, and then performing multi-factor nonlinear regression analysis.

[0034] According to some embodiments of this application, the single-factor regression fitting includes: Based on field monitoring data, single-factor nonlinear regression analysis was conducted on the relationships between the surrounding rock grade and deformation pressure, the tunnel span and deformation pressure, and the bending stiffness of the initial support section and deformation pressure.

[0035] According to some embodiments of this application, the formula for calculating the vertical deformation pressure is as follows: q =3.62 e 0.56S · ω ·2 0.24k in, q This represents the vertical deformation pressure, e is the natural constant, and S represents the surrounding rock grade. ω This represents the span correction factor. k This indicates the flexural stiffness of the initial support section composed of shotcrete and steel frame.

[0036] According to some embodiments of this application, the method further includes performing a goodness-of-fit check on the relational model and adjusting the coefficients of the relational model based on the check result.

[0037] The tunnel deformation pressure calculation method provided in this application can be applied to various tunnel engineering design fields, such as high-speed railway tunnels, highway tunnels, urban subway tunnels, and water conservancy and hydropower diversion tunnels. In the above implementation, when calculating and controlling the design of the tunnel support structure, a comprehensive analysis can be performed based on field monitoring data on the surrounding rock grade, tunnel span, and initial support section bending stiffness. The relationship between deformation pressure and various factors can be established through a multivariate nonlinear regression model. The vertical and horizontal deformation pressures are calculated through the model, thereby achieving accurate prediction of the stress state of the support structure, making the support structure design more consistent with the actual stress conditions, and improving the safety and economy of the design.

[0038] Example 2 As a further optimization of the foregoing embodiments, this application provides a specific implementation method for calculating tunnel deformation pressure. Specifically, the technical solution of this application is as follows: S1. Obtain the basic parameters of the tunnel project, including tunnel depth, surrounding rock grade, and tunnel span. These basic parameters, after data preprocessing such as noise reduction and outlier filtering, serve as the basis for subsequent calculations.

[0039] S2. Determine the initial support scheme for the tunnel. If the initial support includes a steel frame, determine the cross-sectional area of ​​the steel frame, the spacing between the steel frames, and the type and thickness of the shotcrete (hereinafter referred to as shotcrete). Then calculate the bending stiffness of the initial support section. The calculation method is as follows: (1) (2) In the formula: Represents the equivalent elastic modulus; E c This indicates the elastic modulus of shotcrete. A c This represents the cross-sectional area of ​​the sprayed concrete on the equivalent calculation unit section; E s , A s These are the elastic modulus of the steel frame and the cross-sectional area of ​​the steel frame on the equivalent calculation unit section, respectively. I Let the moment of inertia of the cross section be... I = t 3 b / 12, t Indicates the thickness of the spray coating. b This indicates the unit width, which is 1m. k This indicates the bending stiffness of the initial support section composed of sprayed concrete and steel frame.

[0040] S3. Determine the tunnel burial depth, surrounding rock grade, tunnel span, and initial support section bending stiffness range: If the range meets the requirements of general deep-buried tunnels with surrounding rock grades II to V, tunnel span of 8 to 16 m, and initial support section bending stiffness of (0.02 to 5.0) × 10⁻⁶ m, then... 7 N·m 2 For horseshoe-shaped tunnels, the initial support deformation pressure can be calculated using formula (3). If the pressure exceeds this range, the formula should be further analyzed and verified. S4. Calculate the vertical load of deformation pressure: q =3.62 e 0.56S · ω ·2 0.24k (3) In the formula: q —Vertical deformation pressure, in kPa; S —Rock class, such as Class IV rock. S =4; ω —Span correction factor, in meters; where... ω =0.1 B +0.2, B For tunnel span; k —The initial support section consisting of sprayed concrete and steel frame, in units of 10. 7 N·m 2 .

[0041] S5. Calculate the horizontal deformation pressure: H = λq (4) Where H represents the horizontal deformation pressure. λ Indicates the lateral pressure coefficient, Class III surrounding rock. λ <0.25 ， Class IV surrounding rock λ Take a value of 0.25~0.5 ， Class V surrounding rock λ Take a value of 0.5 to 1.0.

[0042] This method considers the influence of support stiffness on deformation pressure when calculating deformation pressure. Based on this formula, the design of tunnel support structures can take into account the influence of parameters such as steel frame spacing and shotcrete intensity on deformation pressure, so that the load borne by the support structure is more in line with reality and the design results are more economical and reliable.

[0043] Example 3 As a further optimization of the preceding embodiments, this application provides a specific implementation method for calculating tunnel deformation pressure, which mainly solves the problem that the current deformation pressure calculation does not consider the stiffness of the support structure, and can further optimize the structure to make it more economical and reasonable.

[0044] I. Univariate Regression Analysis Deformation pressure is mainly reflected in the contact pressure between the surrounding rock and the shotcrete support. Therefore, this invention, through field measurements and data surveys, obtained sample data on the contact pressure between the surrounding rock and the shotcrete support at 217 monitoring sections of 60 tunnels built in China between 2000 and 2025. First, a single-factor nonlinear regression method was used to study the influence of surrounding rock grade, tunnel span, and initial support section bending stiffness on deformation pressure, and the corresponding mathematical relationships were fitted. The core purpose is to eliminate the interference of other variables and analyze the influence of a single factor on deformation pressure, thus providing a foundation for subsequent multivariate nonlinear regression. The specific operation method is as follows: 1. Relationship between surrounding rock grade and deformation pressure To eliminate the influence of tunnel span and initial support section bending stiffness on the surrounding rock deformation pressure value, the average value of surrounding rock deformation pressure at each level in the sample is used as the analysis object to analyze the relationship between the two. Figure 3 As shown, the deformation pressure increases exponentially with the surrounding rock grade, and the fitting formula is q=13.154e 0.52S The correlation coefficient was 0.9865, indicating an extremely high goodness of fit.

[0045] This proves that the higher the surrounding rock grade, the faster the deformation pressure increases, which is consistent with engineering experience and can provide a basis for considering the influence of the surrounding rock grade index in subsequent studies.

[0046] 2. Relationship between tunnel span and deformation pressure To eliminate the influence of tunnel surrounding rock grade and initial support section bending stiffness on deformation pressure, the deformation pressure monitoring samples were classified according to the classification standards for small span, medium span, large span, and extra-large span in the "Tunnel Code," and their average values ​​were used as the analysis object to analyze their influence on deformation pressure. Figure 4 and Figure 5 As shown, the deformation pressure value increases with span in two ways: one is a linear function, with a fitting function of q = 11.82B - 47.17 and a correlation coefficient of 0.994; the other is a power function, with a fitting function of q = 1.95B. 1.5535 The correlation coefficient was 0.989.

[0047] This indicates that the deformation pressure increases significantly as the tunnel span increases, which provides a basis for selecting the span correction coefficient in the final formula, taking into account both linear and nonlinear effects.

[0048] 3. Relationship between initial support stiffness and deformation pressure To eliminate the influence of surrounding rock grade and tunnel span, the average deformation pressure of the flexural stiffness of each initial support section in the sample is used as the analysis object to analyze the relationship between the flexural stiffness of the initial support section and the deformation pressure. Figure 6 and Figure 7 As shown, the deformation pressure increases with the flexural stiffness of the initial support section in two ways: one is a linear function, and the fitted function is... q =33.114 k +32.524, with a correlation coefficient of 0.99; another is the exponential function, with the fitting function being... q =45.642e 0.31k The correlation coefficient was 0.9545.

[0049] This demonstrates that the greater the support stiffness, the greater the deformation pressure. This is because stiffness restricts the deformation of the surrounding rock, resulting in the support bearing a larger load. This provides a basis for choosing an approximate exponential growth in the final formula, reflecting the amplification effect of stiffness on the load.

[0050] The overall technical contribution of the above three analyses is to quantify the influence patterns of surrounding rock grade, span, and initial support section bending stiffness on deformation pressure, laying the foundation for multiple regression.

[0051] II. Multiple Linear Regression After determining the functional relationship between deformation pressure and each factor, a multivariate nonlinear regression method can be used to determine the functional relationship between deformation pressure and multiple factors. Table 1 shows the derivation and establishment of eight deformation pressure calculation formulas considering the influence of tunnel surrounding rock grade, tunnel span, and initial support section bending stiffness.

[0052] Table 1 Deformation-Pressure Regression Analysis

[0053] The formula for calculating the equivalent height with the highest correlation coefficient in Table 1 is taken as the final calculation formula, as follows: Formula for calculating vertical deformation pressure: q =3.62 e 0.56S · ω ·2 0.24k In the formula: q —Vertical deformation pressure, unit kPa; e —Natural constant; S —Rock class, such as Class IV rock, S=4; ω —Span correction factor, ω =0.1B +0.2, B The tunnel span is in meters (m). k —The initial support section composed of sprayed concrete and steel frame has a bending stiffness of 10. 7 N·m 2 The calculation method is shown in Equation (1) and Equation (2).

[0054] Taking double-track railway tunnels with speeds of 250 km / h and 350 km / h as examples, this paper analyzes the differences between the deformation pressure calculation method described in the embodiments of this application and the surrounding rock pressure calculation method for deep-buried tunnels in the "Railway Tunnel Design Code" when calculating the surrounding rock pressure. According to the general reference diagram of railway tunnels, the initial support calculation parameters of deep-buried tunnels with surrounding rock of Class II to V are determined, and the bending stiffness of the initial support section is calculated using formulas (1) and (2). The calculation results are shown in Table 2, and other calculation parameters are shown in Table 3.

[0055] Figure 8 These are curves showing the relationship between calculated pressure and surrounding rock grade using two different methods. According to... Figure 8 It can be seen that the calculated values ​​of deformation pressure are all lower than the loosening pressure in the Tunnel Code for all surrounding rock grades. The specific analysis is shown in Table 4.

[0056] Table 2 Bending Stiffness of Initial Support Section of Deep-Buried Tunnels for 350km / h Double-Track Railways

[0057] Table 3 Calculation parameters

[0058] Table 4 Comparison of calculation results between the two methods

[0059] The deformation pressure of Class II surrounding rock is approximately 40% of that calculated by the "Tunnel Code" formula, while that of Class III to V is approximately 55% to 85%. The difference between the calculation results of the two methods decreases as the surrounding rock class increases. This is because current tunnel construction methods have gradually transitioned from traditional manual and small-scale machinery to large-scale mechanized construction, reducing disturbance to the surrounding rock and protecting its integrity. Furthermore, timely initial support construction limits the further development of surrounding rock deformation and cracks. The implementation of advanced support for weak surrounding rock, and the shift from passive to active support, also improves the self-supporting capacity of the surrounding rock. All these factors limit the conversion of deformation pressure into loosening pressure; therefore, the support structure primarily bears deformation pressure.

[0060] Example 4 As a further optimization of the foregoing embodiments, this application provides a tunnel deformation pressure calculation device, including the following modules: (1) Parameter acquisition module: used to acquire basic parameters of tunnel engineering, including tunnel depth, surrounding rock grade and tunnel span; surrounding rock pressure and support parameters can be collected by field sensors, and the collected data can be preprocessed, including noise reduction, outlier detection and filtering.

[0061] (2) Support scheme module: used to determine the initial support scheme of the tunnel according to the construction design; calculate the bending stiffness of the initial support section according to the elastic modulus and thickness of the shotcrete and the elastic modulus, cross-sectional area and spacing of the steel frame.

[0062] (3) Regression Analysis Module: This module is used to establish a relationship model between deformation pressure and surrounding rock grade, tunnel span, and initial support section flexural stiffness based on historical deformation pressure sample data and using multivariate nonlinear regression analysis. Specifically, it also includes: ① Single-factor analysis submodule, used to fit the individual effects of surrounding rock grade, tunnel span and initial support section bending stiffness on deformation pressure; ② The multi-factor fitting submodule is used to perform multivariate nonlinear regression analysis based on the results of single-factor analysis to obtain a comprehensive relationship model.

[0063] (4) Pressure calculation module: used to calculate the vertical deformation pressure of the target tunnel based on the relational model and the input basic parameters; it also includes a model optimization unit, used to dynamically adjust the coefficients of the relational model according to the goodness of fit, so as to improve the calculation accuracy.

[0064] (5) Result output module: used to output the calculated vertical deformation pressure; the results can be displayed in numerical form, generated into charts or formed into a complete calculation report for designers to refer to.

[0065] Through the collaborative work of the above modules and their sub-modules, this embodiment can realize an automated process from data acquisition, parameter preprocessing, regression analysis, pressure calculation to result output, which significantly improves the accuracy and efficiency of tunnel vertical deformation pressure calculation and provides a reliable basis for the scientific design of tunnel support structures.

[0066] It should be understood that the various modules of the tunnel deformation pressure calculation device provided in the above embodiments are only illustrated by the division of each functional module in the above description. In practical applications, the above functions can be assigned to different functional modules as needed. That is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above.

[0067] The functional modules in the above embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of the embodiments of this application.

[0068] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects.

[0069] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0070] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for calculating tunnel deformation pressure, characterized in that, include: S1. Obtain basic parameters for tunnel engineering, including tunnel depth, surrounding rock grade, and tunnel span; S2. Determine the initial support scheme for the tunnel based on the construction design. The initial support scheme includes shotcrete parameters and steel frame parameters, and calculate the bending stiffness of the initial support section. S3. Based on the deformation pressure sample data, a multivariate nonlinear regression analysis method is used to establish a relationship model between deformation pressure and surrounding rock grade, tunnel span and bending stiffness of initial support section; S4. Calculate the vertical deformation pressure of the tunnel support structure based on the relationship model and the basic parameters, and calculate the horizontal deformation pressure based on the vertical deformation pressure; S5. Output the vertical deformation pressure and horizontal deformation pressure.

2. The method according to claim 1, characterized in that, Step S2 involves calculating the initial support section bending stiffness by determining the elastic modulus and thickness of the shotcrete, as well as the elastic modulus, cross-sectional area, and spacing of the steel frame, and obtaining the initial support section bending stiffness based on the combination relationship between the shotcrete and the steel frame.

3. The method according to claim 1, characterized in that, The relationship model described in step S3 is determined by performing single-factor regression fitting on sample data of surrounding rock grade, tunnel span, and bending stiffness of initial support section, followed by multi-factor nonlinear regression analysis.

4. The method according to claim 3, characterized in that, The single-factor regression fitting includes: Based on field monitoring data, single-factor nonlinear regression analysis was conducted on the relationships between the surrounding rock grade and deformation pressure, the tunnel span and deformation pressure, and the bending stiffness of the initial support section and deformation pressure.

5. The method according to claim 1, characterized in that, The formula for calculating the vertical deformation pressure is as follows: q =3.62 e 0.56S · ω ·2 0.24k in, q The vertical deformation pressure is represented by e, the natural constant is represented by S, and the surrounding rock grade is represented by S. ω denoted by the span correction factor, and k represents the flexural stiffness of the initial support section composed of shotcrete and steel frame.

6. The method according to claim 1, characterized in that, It also includes performing a goodness-of-fit test on the relational model and adjusting the coefficients of the relational model based on the test results.

7. A tunnel deformation pressure calculation device, characterized in that, include: The parameter acquisition module is used to acquire basic parameters of tunnel engineering, including tunnel depth, surrounding rock grade, and tunnel span. The support scheme module is used to determine the initial support scheme for the tunnel based on the construction design and to calculate the bending stiffness of the initial support section. The regression analysis module is used to establish a model of the relationship between deformation pressure and surrounding rock grade, tunnel span and bending stiffness of initial support section based on deformation pressure sample data and multivariate nonlinear regression analysis method. The pressure calculation module is used to calculate the vertical deformation pressure of the tunnel support structure based on the relationship model and the basic parameters, and to calculate the horizontal deformation pressure based on the vertical deformation pressure. The result output module is used to output the vertical deformation pressure and the horizontal deformation pressure.

8. The apparatus according to claim 7, characterized in that, The parameter acquisition module is used to receive monitoring data from field sensors, including denoising and outlier filtering of the data.

9. The apparatus according to claim 7, characterized in that, The regression analysis module includes a single-factor analysis submodule and a multi-factor fitting submodule. The single-factor analysis submodule is used to fit the individual effects of surrounding rock grade, tunnel span, and initial support section bending stiffness on deformation pressure, respectively. The multi-factor fitting submodule is used to perform multivariate nonlinear regression based on the results of the single-factor analysis.

10. The apparatus according to claim 7, characterized in that, The pressure calculation module includes a model optimization unit, which is used to dynamically adjust the coefficients of the relationship model based on the goodness of fit.

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