A method and system for identifying high external water risk of deep-buried lined tunnels

Abstract

The present application relates to underground engineering safety monitoring technical field, disclose a kind of high external water risk identification method and system of deep lining tunnel, to solve the problems of low identification efficiency and poor accuracy of existing method, scheme mainly includes: tunnel geometry, material, ground stress, water pressure, construction and risk discrimination parameter are collected;Determine whether the current working condition is high external water working condition;Establish double-zone plane strain model of surrounding rock and lining collaborative solution, construct non-homogeneous control equation of each area containing pore pressure based on poroelasticity theory and establish pore pressure radial distribution function;Construct each area complex potential function and pore pressure particular solution and superimposed to form analytical function expression;Using internal water pressure load condition, contact surface stress continuity and displacement continuity condition and displacement release coefficient to solve undetermined coefficient, obtain full-field stress displacement distribution;Finally, risk identification index is extracted to carry out crack risk determination and external water sensitivity evaluation.The present application improves the identification efficiency and accuracy, applicable to deep lining tunnel.

Description

Technical Field

[0001] This invention relates to the field of underground engineering safety monitoring technology, specifically to a method and system for identifying high external water risk in deeply buried lined tunnels. Background Technology

[0002] Deeply buried hydraulic tunnels, water diversion tunnels, and other long-term underground water conveyance structures often experience the combined effects of high ground stress and high external water pressure during operation, maintenance, venting, or significant changes in external water head. External water pressure manifests not only as a boundary load acting on the outer surface of the lining but also alters the effective stress state through pore water pressure within the surrounding rock and lining, thus affecting the force transmission characteristics of the rock-lining interface, the degree of local stress concentration in the surrounding rock, and the distribution of local tensile stress in the lining. When the external water head is excessively high or the internal water pressure drops sharply, excessive tensile stress or even cracking may occur in the inner wall of the lining, threatening the long-term safety of the structure. Therefore, accurately assessing the stress-displacement response of the surrounding rock and lining under high external water pressure and identifying hazardous areas is of significant engineering importance for tunnel design, construction, and operation and maintenance.

[0003] The following methods are commonly used for stress analysis of tunnels under high external water conditions:

[0004] One approach is numerical simulation, such as the finite element method and the finite difference method. These methods can establish detailed models of complex geological conditions and structural forms, considering material nonlinearity, contact nonlinearity, and seepage-stress coupling effects, resulting in relatively comprehensive calculations. However, numerical simulation demands significant computational resources and skilled personnel; model building, parameter calibration, and computation are time-consuming, making it unsuitable for rapid screening of numerous working conditions and parameter sensitivity analysis during the design phase.

[0005] Second, there are empirical formulas and reduction factor methods. These methods consider the sharing effect of external water pressure on the surrounding rock by multiplying the external water pressure by a certain reduction factor, or by using simplified thick-walled cylindrical theoretical formulas to estimate the internal forces of the lining. While these methods are simple to calculate, the selection of the reduction factor often relies on engineering experience and lacks a unified mechanical theoretical basis. This makes it difficult to accurately reflect the actual stress state under different surrounding rock conditions and water head conditions, and especially difficult to pinpoint the dangerous location of the lining.

[0006] Thirdly, there are simplified analytical methods that only consider boundary water pressure. These methods treat external water pressure as a surface force acting on the outer wall of the lining, neglecting the distribution of pore water pressure within the surrounding rock and lining and its impact on effective stress. While these methods are computationally efficient, they fail to accurately reflect the mechanism by which the pore water pressure field alters the stress state of the surrounding rock and lining under high external water conditions, resulting in insufficient computational accuracy and difficulty in determining the specific location of hazardous areas.

[0007] In summary, numerical simulation methods are insufficient to meet the needs of rapid screening in the design phase, empirical formulas and reduction factor methods lack a unified mechanical theoretical basis, and simplified analytical methods fail to truly reflect the intrinsic mechanism of pore water pressure field. Furthermore, none of the above methods treat the surrounding rock and lining as a unified mechanical system for collaborative solution, making it difficult to achieve accurate analysis of stress and displacement and precise location of dangerous areas while ensuring computational efficiency. Summary of the Invention

[0008] This invention aims to solve the problems of low identification efficiency and poor accuracy in existing methods for identifying high external water risk in deeply buried lined tunnels, and proposes a method and system for identifying high external water risk in deeply buried lined tunnels.

[0009] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0010] In a first aspect, the present invention provides a method for identifying high external water risk in deeply buried lined tunnels, the method comprising:

[0011] Step 1: Collect the input parameters required for risk identification of deeply buried lined tunnels. The input parameters include: geometric parameters, material parameters, ground stress parameters, water pressure parameters, construction parameters, and risk discrimination parameters.

[0012] Step 2: Determine whether the current operating condition is a high external water condition based on the water pressure parameters. If it is, proceed to the next step.

[0013] Step 3: Use the geometric parameters to establish a dual-region plane strain model for the coordinated solution of the surrounding rock region and the lining region;

[0014] Step 4: Using the material parameters and geostress parameters, based on the pore elasticity theory, pore water pressure is introduced as an internal field variable into the constitutive relations of the surrounding rock and the lining, respectively. In the dual-region plane strain model, non-homogeneous control equations with pore pressure terms in the surrounding rock region and non-homogeneous control equations with pore pressure terms in the lining region are constructed, respectively.

[0015] Step 5: Using the geometric parameters and water pressure parameters, establish the radial distribution function of pore water pressure in the surrounding rock area and the radial distribution function of pore water pressure in the lining area under the quasi-steady-state seepage assumption, respectively.

[0016] Step 6: Based on the non-homogeneous governing equations of the pore pressure terms in the surrounding rock region and the pore pressure terms in the lining region, construct the complex potential function of the surrounding rock region and the complex potential function of the lining region, respectively. Based on the radial distribution function of pore water pressure in the surrounding rock region and the radial distribution function of pore water pressure in the lining region, construct the particular solution of pore pressure in the surrounding rock region and the particular solution of pore pressure in the lining region, respectively. Superimpose the complex potential function of each region with the corresponding particular solution of pore pressure to form the analytical function expression of the pore pressure terms in each region.

[0017] Step 7: Using the water pressure parameters, set the internal water pressure load condition at the inner boundary of the lining; using the geometric parameters, set the stress continuity condition and displacement continuity condition at the contact surface between the surrounding rock and the lining; the displacement continuity condition introduces the displacement release coefficient from the construction parameters.

[0018] Step 8: Substitute the internal water pressure load condition, stress continuity condition, and displacement continuity condition including displacement release coefficient into the analytical function expression of the pore pressure term in the surrounding rock area and the analytical function expression of the pore pressure term in the lining area, respectively, to form a closed system of equations with undetermined coefficients and solve it to obtain the analytical function coefficients.

[0019] Step 9: Based on the analytical function coefficients and the analytical function expressions of the pore pressure terms in each region, calculate the whole-field radial stress, tangential stress, shear stress, radial displacement, and tangential displacement in the surrounding rock region and the lining region to form the whole-field stress and displacement distribution;

[0020] Step 10: Extract risk identification indicators based on the full-field stress and displacement distribution, compare the risk identification indicators with the risk discrimination parameters, and output the high external water risk area identification results and external water sensitivity evaluation results.

[0021] Further, in step 2, determining whether the current operating condition is a high external water condition based on the water pressure parameters specifically includes:

[0022] Calculate the head difference based on the external water head and internal water head in the aforementioned water pressure parameters: ,in, Indicates the difference in water head. Indicates external water head. Indicates the internal water head;

[0023] Calculate the pore pressure difference based on the far-field pore pressure and the inner boundary pore pressure in the aforementioned water pressure parameters: ,in, Indicates the orifice pressure difference. Indicates far-field pore pressure, Indicates the pore pressure at the inner boundary;

[0024] The high external water condition meets at least one of the following conditions:

[0025] The head difference is positive, meaning the external water head is higher than the internal water head.

[0026] The pore pressure difference is positive, meaning that the far-field pore pressure is higher than the inner boundary pore pressure.

[0027] Under maintenance, venting, or low internal water pressure conditions, the contribution of the external water pressure calculated based on the head difference or pore pressure difference to the change of the target stress displacement index reaches a preset threshold. The target stress displacement index is the maximum tangential stress of the inner boundary of the lining or the radial displacement of the inner boundary of the lining.

[0028] Furthermore, in step 4, the non-homogeneous governing equation for the pore pressure term in the surrounding rock region is:

[0029] ;

[0030] The non-homogeneous governing equation for the lining region, including the pore pressure term, is:

[0031] ;

[0032] in, , , , , , , , , Represents the Biot coefficient of the surrounding rock. Indicates the Poisson's ratio of the surrounding rock. Indicates the Biot coefficient of the lining. Indicates the Poisson's ratio of the lining. This represents the pore pressure coefficient of the surrounding rock. This represents the pore pressure coefficient of the lining. Indicates the pore water pressure in the surrounding rock region. Indicates the pore water pressure in the lining area. For the Laplace operator, For a bitone operator, This represents the total stress function in the surrounding rock region. This represents the total stress function in the lining area. , This represents the stress function decomposition terms in the surrounding rock region. , This represents the stress function decomposition term in the lining area.

[0033] Furthermore, in step 5, the radial distribution function of pore water pressure in the surrounding rock region is:

[0034] ;

[0035] The radial distribution function of pore water pressure in the lining region is:

[0036] ;

[0037] in, Indicates the pore water pressure in the surrounding rock region. Indicates the pore water pressure in the lining area. , , These represent the inner radius of the lining, the radius of the contact surface between the surrounding rock and the lining, and the radius of the far-field outer boundary, respectively, in the geometric parameters. , , , These represent the far-field pore pressure, inner boundary pore pressure, surrounding rock side contact pore pressure, and lining side contact pore pressure, respectively. Indicates radial position coordinates, It represents the natural logarithm.

[0038] Furthermore, in step 6, the complex potential function of the surrounding rock region is expressed using a Taylor series as follows:

[0039] , ;

[0040] The complex potential function of the lining region is expressed using Laurent series:

[0041] , ;

[0042] in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. , , , , , Denotes the undetermined complex potential coefficient. Represents the order of a series. For complex plane coordinates, The imaginary unit, , Represents rectangular coordinate components;

[0043] The pore pressure specific solution of the surrounding rock region for:

[0044] ;

[0045] The pore pressure particular solution of the lining region for:

[0046] ;

[0047] in, This represents the pore pressure coefficient of the surrounding rock. This represents the pore pressure coefficient of the lining. This represents a constant term.

[0048] Furthermore, in step 7, the internal water pressure load condition is:

[0049] ;

[0050] in, Indicates the radial stress of the lining. Indicates the shear stress of the lining. The imaginary unit, Indicates taking the real part, Represents the complex potential function of the lining The first derivative, Represents the complex potential function of the lining The second derivative, For complex plane coordinates, The imaginary unit, , Represents rectangular coordinate components. Represents the angle in polar coordinates. Represents a complex exponential function. This represents the pore pressure coefficient of the lining. Indicates the pore water pressure in the lining area. This refers to the inner boundary pore pressure in the water pressure parameters. Represents the pore pressure specific solution of the lining region; radial position coordinates at the inner boundary of the lining. , This represents the inner radius of the lining in the geometric parameters;

[0051] The stress continuity condition is:

[0052] ;

[0053] in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. express conjugate, express conjugate, express conjugate, express conjugate, Represents the pore pressure specific solution of the lining area; radial position coordinates at the surrounding rock-lining interface. , Indicates the radius of the contact surface between the surrounding rock and the lining;

[0054] The displacement continuity condition is:

[0055]

[0056] ;

[0057] in, Indicates the radial displacement of the surrounding rock region. This indicates the tangential displacement of the surrounding rock region. This represents the displacement release coefficient in the construction parameters. This represents the shear modulus of the surrounding rock. Indicates the shear modulus of the lining. Represents the Kolosov constant of the surrounding rock. This represents the Kolosov constant for the lining. Indicates the Poisson's ratio of the surrounding rock. Indicates the Poisson's ratio of the lining. Represents complex plane coordinates The conjugate complex coordinates, Represents the complex potential function of the surrounding rock After differentiation, in conjugate complex coordinates Take the value at the given point, then take the conjugate; Represents the complex potential function of the surrounding rock In conjugate complex coordinates Take the value at the given location and take its conjugate; Represents the complex potential function of the lining After differentiation, in conjugate complex coordinates Take the value at the given point, then take the conjugate; Represents the complex potential function of the lining In conjugate complex coordinates Take the value at the given location and take the conjugate.

[0058] Further, in step 8, the internal water pressure load condition, stress continuity condition and displacement continuity condition including displacement release coefficient are substituted into the analytical function expression of the pore pressure term in the surrounding rock area and the analytical function expression of the pore pressure term in the lining area, respectively. The first three terms are retained to form a closed system of equations with undetermined coefficients and then solved.

[0059] The closed system of equations with undetermined coefficients contains 9 unknown coefficients and 9 equations. The coefficients of the analytic function obtained by solving it are: ,in, Represents the coefficients of an analytic function. , , These represent the first three undetermined coefficients of the complex potential function of the surrounding rock region. , , , , , These represent the first three undetermined coefficients of the complex potential function of the lining region. This indicates the matrix transpose.

[0060] Furthermore, in step 9, the calculation method for the overall stress and displacement distribution includes:

[0061] Step 91: Based on the analytical function coefficients, combined with the far-field principal stress reference value and lateral pressure coefficient in the geostress parameters, and the radius of the rock-lining contact surface in the geometric parameters, calculate the complex potential function of the surrounding rock region and the complex potential function of the lining region.

[0062] The complex potential function of the surrounding rock region is:

[0063] ;

[0064] ;

[0065] The complex potential function of the lining region is:

[0066] ;

[0067] ;

[0068] in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. , This represents the intermediate variable of the far-field stress. , , This represents the reference value of the far-field principal stress in the geostress parameters. This represents the lateral pressure coefficient in the geostress parameters. This represents the radius of the rock-lining contact surface in the geometric parameters. For complex plane coordinates, The imaginary unit, , Represents rectangular coordinate components;

[0069] Step 92: Based on the total stress function of the surrounding rock area Calculate the stress components of the surrounding rock region in rectangular coordinates:

[0070] ;

[0071] ;

[0072] ;

[0073] in, , This represents the normal stress components in rectangular coordinates of the surrounding rock region. This represents the shear stress components in the surrounding rock region. This represents the total stress function in the surrounding rock region. , Represents the stress function decomposition terms in the surrounding rock region;

[0074] Step 93: Based on the total stress function of the lining area Calculate the stress components of the lining area in rectangular coordinates:

[0075] ;

[0076] ;

[0077] ;

[0078] in, , This represents the normal stress components in rectangular coordinates of the lining area. This represents the shear stress components in the lining area. This represents the total stress function in the lining area. , This represents the stress function decomposition terms in the lining area;

[0079] Step 94: Calculate the displacement components of the surrounding rock region in rectangular coordinates based on the complex potential function of the surrounding rock region.

[0080] ;

[0081] in, This represents the shear modulus of the surrounding rock. , This represents the displacement components in rectangular coordinates of the surrounding rock region. Indicates the Poisson's ratio of the surrounding rock;

[0082] Step 95: Calculate the displacement components of the lining region in rectangular coordinates based on the complex potential function of the lining region.

[0083] ;

[0084] in, Indicates the shear modulus of the lining. , This represents the displacement components of the lining area in rectangular coordinates. Indicates the Poisson's ratio of the lining;

[0085] Step 96: Convert the stress components in rectangular coordinates. , , , , , After coordinate transformation, the full-field radial stress, tangential stress, and shear stress in the surrounding rock region and lining region are obtained; the displacement components in rectangular coordinates are then transformed. , , , After coordinate transformation, the full-field radial and tangential displacements of the surrounding rock area and the lining area are obtained.

[0086] Furthermore, step 10 specifically includes:

[0087] Step 101: Determine the maximum tangential stress index and corresponding critical azimuth angle at the inner boundary of the lining based on the tangential stress distribution at the inner boundary of the lining.

[0088] ;

[0089] ;

[0090] in, This indicates the maximum tangential stress index at the inner boundary of the lining. Indicates the angle at the inner boundary of the lining. Tangential stress at the location, radial position coordinates at the inner boundary of the lining. , This represents the inner radius of the lining in the geometric parameters. Indicates the angle Take the maximum value. Indicates the danger azimuth. This represents the angle at which the function reaches its maximum value. Values;

[0091] Step 102: The maximum tangential stress at the inner boundary of the lining... Compared with the lining compressive strength limit in the risk discrimination parameters Compare; when At that time, determine the dangerous azimuth angle. There is a risk of fracturing at the location; otherwise, it is determined that there is no risk of fracturing at the inner boundary of the lining.

[0092] Step 103: According to different external water head The maximum tangential stress at the inner boundary of the lining under the specified conditions Rate of change determines external water sensitivity index :

[0093] ;

[0094] in, and This indicates two different external water head values. and This represents the maximum tangential stress at the inner boundary of the lining under the corresponding external water head.

[0095] Step 104: The external water sensitivity index Compared with the external water sensitivity threshold in the risk discrimination parameters Comparison; when the external water sensitivity index Exceeding the aforementioned external water sensitivity threshold If the condition is positive, it is determined to be a water-sensitive condition; otherwise, it is determined to be a non-water-sensitive condition.

[0096] In a second aspect, the present invention provides a high external water risk identification system for deeply buried lined tunnels, used to implement the high external water risk identification method for deeply buried lined tunnels as described in the first aspect, the system comprising:

[0097] The parameter acquisition module is used to collect the input parameters required for risk identification of deeply buried lined tunnels. The input parameters include: geometric parameters, material parameters, ground stress parameters, water pressure parameters, construction parameters, and risk discrimination parameters.

[0098] The operating condition determination module is used to determine whether the current operating condition is a high external water condition based on the water pressure parameters. If the condition is determined to be a high external water condition, the subsequent steps are performed.

[0099] The model building module is used to establish a dual-region plane strain model for collaborative solution of the surrounding rock region and the lining region using the geometric parameters.

[0100] The governing equation construction module is used to utilize the material parameters and geostress parameters, based on the pore elasticity theory, and introduce pore water pressure as an internal field variable into the constitutive relations of the surrounding rock and the lining, respectively, to construct non-homogeneous governing equations with pore pressure terms in the surrounding rock region and non-homogeneous governing equations with pore pressure terms in the lining region in the dual-region plane strain model.

[0101] The pore pressure distribution establishment module is used to establish the radial distribution function of pore water pressure in the surrounding rock area and the radial distribution function of pore water pressure in the lining area under the quasi-steady-state seepage assumption using the geometric parameters and water pressure parameters.

[0102] The analytical function construction module is used to construct the complex potential function of the surrounding rock region and the complex potential function of the lining region based on the non-homogeneous governing equations of the pore pressure term in the surrounding rock region and the non-homogeneous governing equations of the pore pressure term in the lining region, respectively. Based on the radial distribution function of pore water pressure in the surrounding rock region and the radial distribution function of pore water pressure in the lining region, it constructs the particular solution of pore pressure in the surrounding rock region and the particular solution of pore pressure in the lining region, respectively. The complex potential function of each region is superimposed with the corresponding particular solution of pore pressure to form the analytical function expression of the pore pressure term in each region.

[0103] The condition setting module is used to set internal water pressure load conditions at the inner boundary of the lining using the water pressure parameters, and to set stress continuity conditions and displacement continuity conditions at the contact surface between the surrounding rock and the lining using the geometric parameters. The displacement continuity condition incorporates the displacement release coefficient from the construction parameters.

[0104] The equation solving module is used to substitute the internal water pressure load condition, stress continuity condition, and displacement continuity condition including displacement release coefficient into the analytical function expression of the pore pressure term in the surrounding rock area and the analytical function expression of the pore pressure term in the lining area, respectively, to form a closed equation system with undetermined coefficients and solve it to obtain the analytical function coefficients.

[0105] The stress-displacement calculation module is used to calculate the whole-field radial stress, tangential stress, shear stress, radial displacement, and tangential displacement of the surrounding rock area and the lining area based on the analytical function coefficients and the analytical function expression of the pore pressure term in each region, thus forming the whole-field stress and displacement distribution;

[0106] The risk identification module is used to extract risk identification indicators based on the stress and displacement distribution across the entire field, compare the risk identification indicators with the risk discrimination parameters, and output the identification results of high external water risk areas and the evaluation results of external water sensitivity.

[0107] The beneficial effects of this invention are as follows: By establishing a dual-region plane strain model for the coordinated solution of the surrounding rock and lining regions, this invention directly solves the non-homogeneous governing equations containing pore pressure terms using the complex variable function method. This allows for rapid acquisition of the stress and displacement distribution across the entire field of the surrounding rock and lining without requiring extensive numerical iterations, significantly improving the efficiency of multi-condition screening and parameter sensitivity analysis during the design phase. Furthermore, based on pore elasticity theory, this invention introduces pore water pressure as an internal field variable into the constitutive relationship of the surrounding rock and lining. Combining the radial distribution function of pore water pressure under the quasi-steady-state seepage assumption, it constructs an analytical function expression formed by the superposition of complex potential functions and particular solutions of pore pressure in each region. A closed system of equations is then solved using internal water pressure load conditions, contact surface stress continuity and displacement continuity conditions, and displacement release coefficients. This accurately reflects the mechanism by which the pore water pressure field changes the effective stress state under high external water pressure and the collaborative stress relationship between the surrounding rock and lining, effectively improving the accuracy of risk identification. Furthermore, this invention extracts the full-field stress-displacement calculation results as risk identification indicators and compares them with risk discrimination parameters to output the identification results of high external water risk areas, providing a clear basis for risk judgment in engineering design. Attached Figure Description

[0108] Figure 1 A flowchart illustrating the high external water risk identification method for deeply buried lined tunnels provided in this embodiment;

[0109] Figure 2 A schematic diagram of the structure of the dual-region plane strain model provided in the embodiment;

[0110] Figure 3 A schematic diagram of the pore water pressure radius distribution with radial position provided for the embodiment;

[0111] Figure 4 A schematic diagram of the distribution of circumferential stress at the inner boundary of the lining as a function of angle, provided for an embodiment;

[0112] Figure 5 A schematic diagram of the distribution of circumferential stress at the outer boundary of the lining as a function of angle, provided for an embodiment;

[0113] Figure 6 A schematic diagram of the distribution of radial stress in the vertical direction with radial position provided for an embodiment;

[0114] Figure 7 This is a schematic diagram of the high external water risk identification system for deeply buried lined tunnels provided in the embodiment. Detailed Implementation

[0115] Existing numerical simulation methods are time-consuming, making them unsuitable for rapid screening of numerous working conditions and parameter sensitivity analysis during the design phase. The selection of reduction coefficients in empirical formulas and reduction coefficient methods lacks a unified mechanical theoretical basis, making it difficult to accurately reflect the actual stress state under different surrounding rock and water head conditions and to locate the dangerous position of the lining. Simplified analytical methods that only consider boundary water pressure fail to introduce pore water pressure as an internal field variable into the constitutive relationship between the surrounding rock and the lining, resulting in limited calculation accuracy and the inability to give the specific location of the dangerous area.

[0116] Based on this, the technical solution of this invention is proposed. In this invention, geometric parameters, material parameters, geostress parameters, water pressure parameters, construction parameters, and risk assessment parameters of a deeply buried lining tunnel are collected. After determining the current working condition to be a high external water condition, a dual-region plane strain model for collaborative solution of the surrounding rock and lining regions is established. This provides a complete input foundation for subsequent analytical solutions, avoiding the time consumption of repeatedly modeling complex geological models. Based on this, this invention, using pore elasticity theory, introduces pore water pressure as an internal field variable into the constitutive relations of the surrounding rock and lining respectively, constructing non-homogeneous control equations containing pore pressure terms for each region. Under the quasi-steady-state seepage assumption, radial distribution functions of pore water pressure in each region are established, thereby realistically reflecting the effect of the pore water pressure field on the surrounding rock and lining under high external water conditions. The invention further explores the mechanism of force state change. It constructs complex potential functions for each region and their corresponding pore pressure particular solutions, superimposing them to form an analytical function expression containing pore pressure terms. Utilizing the internal water pressure load conditions at the inner boundary of the lining, the stress continuity conditions and displacement continuity conditions at the rock-lining contact surface, and the displacement release coefficient in the construction parameters, it forms a closed set of equations with undetermined coefficients and solves them. This yields the stress and displacement distribution across the entire rock and lining field, realizing the collaborative stress analysis between the two regions and the quantitative characterization of construction lag effects, effectively improving the accuracy of risk identification. Finally, by extracting the stress and displacement distribution across the entire field as risk identification indicators and comparing them with risk discrimination parameters, the invention outputs the identification results of high external water risk areas, providing a clear basis for risk judgment in engineering design.

[0117] The technical solutions in this embodiment will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0118] Figure 1 A flowchart illustrating a method for identifying high external water risk in deeply buried lined tunnels is shown. Please refer to [link / reference]. Figure 1 The method includes the following steps:

[0119] Step 1: Collect the input parameters required for risk identification of deeply buried lined tunnels. The input parameters include: geometric parameters, material parameters, ground stress parameters, water pressure parameters, construction parameters, and risk discrimination parameters.

[0120] Specifically, this step aims to provide a complete set of input parameters for subsequent modeling and solving. Specifically, geometric parameters include the inner radius of the lining, the radius of the rock-lining contact surface, and the radius of the far-field outer boundary, used to define the spatial extent of the rock and lining regions; material parameters include the elastic modulus, Poisson's ratio, and Biot coefficient of the rock and lining, used to describe the mechanical properties of the two regions; geostress parameters include the far-field principal stress reference value and the lateral pressure coefficient, used to characterize the initial geostress field conditions; water pressure parameters include external water head, internal water head, far-field pore pressure, inner boundary pore pressure, and contact pore pressure, used to determine high external water conditions and pore water pressure boundaries; construction parameters include the displacement release coefficient, used to quantify the release ratio of rock deformation before lining support formation; risk assessment parameters include the tensile strength limit of the lining and the external water sensitivity threshold, used as the basis for judgment in the subsequent risk identification stage. The above parameters can be obtained through engineering geological survey reports, indoor rock mechanics tests, design documents, and field monitoring data.

[0121] Step 2: Determine whether the current operating condition is a high external water condition based on the water pressure parameters. If it is, proceed to the next step.

[0122] In this embodiment, determining whether the current operating condition is a high external water condition based on the water pressure parameters specifically includes:

[0123] Calculate the head difference based on the external water head and internal water head in the aforementioned water pressure parameters: ,in, Indicates the difference in water head. Indicates external water head. Indicates the internal water head;

[0124] Calculate the pore pressure difference based on the far-field pore pressure and the inner boundary pore pressure in the aforementioned water pressure parameters: ,in, Indicates the orifice pressure difference. Indicates far-field pore pressure, Indicates the pore pressure at the inner boundary;

[0125] The high external water condition meets at least one of the following conditions:

[0126] The head difference is positive, meaning the external water head is higher than the internal water head.

[0127] The pore pressure difference is positive, meaning that the far-field pore pressure is higher than the inner boundary pore pressure.

[0128] Under maintenance, venting, or low internal water pressure conditions, the contribution of the external water pressure calculated based on the head difference or pore pressure difference to the change of the target stress displacement index reaches a preset threshold. The target stress displacement index is the maximum tangential stress of the inner boundary of the lining or the radial displacement of the inner boundary of the lining.

[0129] Specifically, this step is used to determine whether the current operating condition is a high external water condition that requires risk identification, in order to determine whether to trigger the subsequent assessment process.

[0130] In this embodiment, the judgment is made from two aspects: head difference and pore pressure difference. On the one hand, the difference between the external water head and the internal water head is used to determine the head difference between the inside and outside of the lining. The larger the difference, the more significant the effect of the external water pressure on the lining. On the other hand, the difference between the far-field pore pressure and the inner boundary pore pressure is used to determine the overall driving potential of the pore water pressure field inside the surrounding rock and the lining. The larger the difference, the stronger the influence of seepage on the effective stress state of the surrounding rock and the lining.

[0131] Based on this, a high external water condition is determined if at least one of the following conditions is met: (1) the external water head is higher than the internal water head, indicating that the lining is subjected to seepage pressure from the outside to the inside; (2) the far-field pore pressure is higher than the inner boundary pore pressure, indicating that there is a pore water pressure driving potential in the surrounding rock and the lining pointing into the tunnel; (3) under maintenance, venting or low internal water pressure conditions, the contribution of the external water pressure calculated based on the above head difference or pore pressure difference to the change of the maximum tangential stress of the inner boundary of the lining or the radial displacement of the inner boundary of the lining reaches the preset threshold. Under such conditions, the decrease in internal water pressure leads to the relative dominance of external water pressure, and the effect of high external water needs to be given special attention.

[0132] This embodiment uses the above-mentioned judgment mechanism to screen out the working conditions that require risk identification, avoiding the need to perform the subsequent complete analysis process for all working conditions, thereby further improving the efficiency of risk identification without affecting the accuracy of the judgment.

[0133] Step 3: Use the geometric parameters to establish a dual-region plane strain model for the coordinated solution of the surrounding rock region and the lining region.

[0134] In this embodiment, a dual-region plane strain model for co-solving the surrounding rock region and the lining region is constructed based on the collected geometric parameters. Please refer to [link / reference]. Figure 2 Geometric parameters include the inner radius of the lining. Radius of the contact surface between the surrounding rock and the lining and far-field outer boundary radius The above parameters together define the spatial extent of the two regions: the surrounding rock region is... An infinite or semi-infinite domain, the lining region is The model establishes a finite-thickness annular region. Based on this, both the surrounding rock and the lining are considered homogeneous, isotropic, linearly elastic, and permeable media. The stress state of the surrounding rock and lining is simplified to a plane strain problem, assuming the tunnel extends infinitely along the axial direction and that each section perpendicular to the axis has the same stress-displacement distribution. Through the establishment of this model, the surrounding rock and lining are integrated into two interacting regions within the same mechanical system, providing a unified geometric basis for subsequently establishing the governing equations and contact surface continuity conditions for the two regions.

[0135] Step 4: Using the material parameters and geostress parameters, based on the pore elasticity theory, pore water pressure is introduced as an internal field variable into the constitutive relations of the surrounding rock and the lining, respectively. In the dual-region plane strain model, non-homogeneous control equations with pore pressure terms in the surrounding rock region and non-homogeneous control equations with pore pressure terms in the lining region are constructed, respectively.

[0136] Specifically, this step aims to transform pore water pressure from an external boundary load in traditional methods into an internal field variable affecting the effective stress state of the material, thereby truly reflecting the actual stress mechanism of the surrounding rock and lining under high external water pressure. In practice, firstly, based on the collected parameters of the surrounding rock and lining materials (including elastic modulus, Poisson's ratio, and Biot coefficient) and geostress parameters, pore water pressure is introduced into the constitutive relation of the surrounding rock and lining according to Biot's pore elasticity theory. Then, based on the dual-region plane strain model established in step 3, non-homogeneous governing equations containing pore pressure terms are constructed for the surrounding rock region and the lining region, respectively.

[0137] In this embodiment, the non-homogeneous governing equation for the pore pressure term in the surrounding rock region is:

[0138] ;

[0139] The non-homogeneous governing equation for the lining region, including the pore pressure term, is:

[0140] ;

[0141] in, , , , , , , , , Represents the Biot coefficient of the surrounding rock. Indicates the Poisson's ratio of the surrounding rock. Indicates the Biot coefficient of the lining. Indicates the Poisson's ratio of the lining. This represents the pore pressure coefficient of the surrounding rock. This represents the pore pressure coefficient of the lining. Indicates the pore water pressure in the surrounding rock region. Indicates the pore water pressure in the lining area. For the Laplace operator, For a bitone operator, This represents the total stress function in the surrounding rock region. This represents the total stress function in the lining area. , This represents the stress function decomposition terms in the surrounding rock region. , This represents the stress function decomposition term in the lining area.

[0142] The left-hand side of the above governing equations consists of standard biharmonic operator terms, which describe the spatial distribution of the stress function; the right-hand side consists of non-homogeneous terms, representing additional stress source terms caused by the pore water pressure gradient. In other words, the left-hand side describes the stress distribution within the surrounding rock and lining, while the right-hand side describes the additional stress sources caused by the spatial distribution of pore water pressure (i.e., the pore pressure gradient).

[0143] The strength of the non-homogeneous term is determined by both the Biot coefficient and Poisson's ratio of the material: the Biot coefficient reflects the influence of pore water pressure changes on the effective stress, while the Poisson's ratio reflects the volume change characteristics of the material under stress. For ease of solution, the total stress function is decomposed into homogeneous and non-homogeneous parts: homogeneous part... and It satisfies the standard biharmonic equations and is used to describe the stress distribution without considering pore water pressure; nonhomogeneous part and The coefficient specifically used to characterize the contribution of pore water pressure to the total stress function is denoted as the proportionality coefficient to pore water pressure. and The above decomposition transforms the complex nonhomogeneous problem containing the pore pressure term into a superposition problem that can be solved term by term, providing a mathematical foundation for constructing analytical solutions using the complex variable function method.

[0144] In practical applications, when there is a difference between the far-field pore pressure and the contact pore pressure, the non-homogeneous term on the right side is not zero, thus generating an additional stress increment inside the surrounding rock and lining. When there is no head difference, the right-side term disappears, and the governing equation degenerates into the homogeneous biharmonic equation in classical elasticity, that is, the conventional surrounding rock-lining stress analysis without considering the influence of external water pressure.

[0145] Step 5: Using the geometric parameters and water pressure parameters, establish the radial distribution function of pore water pressure in the surrounding rock area and the radial distribution function of pore water pressure in the lining area under the quasi-steady-state seepage assumption.

[0146] Specifically, this step is used to establish the pore water pressure distribution function within the surrounding rock and lining regions, providing a clear spatial distribution expression for the pore pressure in the non-homogeneous governing equation containing the pore pressure term in step 4. In this embodiment, it is assumed that the seepage in both the surrounding rock and lining satisfies the quasi-steady-state seepage condition, i.e., the pore water pressure changes only radially and does not change with time, and the pore pressure is equal in all directions at the same radius, thus simplifying the three-dimensional seepage problem into a radial one-dimensional problem. Under the above assumptions, the pore water pressure in both the surrounding rock and lining regions is described using a radial logarithmic function form satisfying the Laplace equation.

[0147] In this embodiment, the radial distribution function of pore water pressure in the surrounding rock region is:

[0148] ;

[0149] The radial distribution function of pore water pressure in the lining region is:

[0150] ;

[0151] in, Indicates the pore water pressure in the surrounding rock region. Indicates the pore water pressure in the lining area. , , These represent the inner radius of the lining, the radius of the contact surface between the surrounding rock and the lining, and the radius of the far-field outer boundary, respectively, in the geometric parameters. , , , These represent the far-field pore pressure, inner boundary pore pressure, surrounding rock side contact pore pressure, and lining side contact pore pressure, respectively. Indicates radial position coordinates, It represents the natural logarithm.

[0152] Please see Figure 3 Specifically, the pore pressure distribution in the surrounding rock region varies from the pore pressure at the far-field outer boundary. Contact face pressure with surrounding rock Common control: The pore pressure at the far-field outer boundary is a known value. The pore pressure on the surrounding rock side of the rock-lining contact surface is Surrounding rock area ( The pore pressure within the cavity is radially from Logarithmic increase to The pore pressure distribution in the lining area is determined by the pore pressure at the lining side contact points. and inner boundary pore pressure Common control: The pore pressure at the inner boundary of the lining is equal to the internal water pressure. The pore pressure on the lining side of the contact surface is Lining area ( The pore pressure within the cavity is radially from Logarithmic increase to .

[0153] It should be noted that the contact surface pressure of the surrounding rock side is... Contact hole with lining side pressure The values ​​may differ, and the difference reflects the pore pressure continuity at the interface between the surrounding rock and the lining. The specific values ​​need to be determined based on the actual hydraulic boundary conditions and the permeability characteristics of the interface. The two functions mentioned above determine the pore water pressure values ​​at any radius within the surrounding rock region and the lining region, respectively, providing input for subsequent construction of pore pressure particular solutions for each region.

[0154] Step 6: Based on the non-homogeneous governing equations of the pore pressure terms in the surrounding rock region and the pore pressure terms in the lining region, construct the complex potential function of the surrounding rock region and the complex potential function of the lining region, respectively. Based on the radial distribution function of pore water pressure in the surrounding rock region and the radial distribution function of pore water pressure in the lining region, construct the particular solutions of pore pressure in the surrounding rock region and the particular solutions of pore pressure in the lining region, respectively. Superimpose the complex potential function of each region with the corresponding particular solution of pore pressure to form the analytical function expression of the pore pressure terms in each region.

[0155] In this embodiment, the complex potential function of the surrounding rock region is represented by a Taylor series as follows:

[0156] , ;

[0157] The complex potential function of the lining region is expressed using Laurent series:

[0158] , ;

[0159] in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. , , , , , Denotes the undetermined complex potential coefficient. Represents the order of a series. For complex plane coordinates, The imaginary unit, , Represents rectangular coordinate components;

[0160] The pore pressure specific solution of the surrounding rock region for:

[0161] ;

[0162] The pore pressure particular solution of the lining region for:

[0163] ;

[0164] in, This represents the pore pressure coefficient of the surrounding rock. This represents the pore pressure coefficient of the lining. This represents a constant term.

[0165] Specifically, this step is used to construct analytical functions for the pore pressure terms in the surrounding rock region and the lining region. In the complex variable method, the stress and displacement of a plane elastic problem can be uniquely determined by two complex potential functions (also called analytical functions): denoted as... and ,in The main terms of the stress field and the displacement field are controlled. The auxiliary terms controlling the stress field and the rotational components of the displacement field are used. Therefore, by obtaining the specific forms of these two complex potential functions, the stress-displacement distribution across the entire field can be obtained.

[0166] In this embodiment, the surrounding rock region is an infinite domain ( The stress within it tends to the geostress field at infinity, therefore the complex potential function of the surrounding rock region adopts a Taylor series form containing only negative power terms: the negative power terms automatically decay to zero at infinity, satisfying the geostress boundary conditions at infinity; the lining region is a finite-thickness annular domain ( The stress within the annular region is simultaneously constrained by the inner boundary and the contact surface. Therefore, the complex potential function of the lining region adopts a Laurent series form containing both positive and negative power terms: the positive and negative power terms are used to match the constraint conditions at the inner and outer boundaries, respectively. The coefficients before each term in the above series expansion... All of these are unknown quantities, which will be determined later through boundary conditions and contact conditions.

[0167] Meanwhile, to account for the influence of pore water pressure, the radial distribution function of pore pressure established in step 5 needs to be substituted into the non-homogeneous part of the stress function in step 4. equation Solving the problem yields particular solutions for pore pressure in each region. and This particular solution reflects the direct contribution of the spatial distribution of pore water pressure to the stress field: the logarithmic change of pore pressure along the radial direction (from step 5) and (Given) After two integrations, the following is generated: Item and The particular solution form of the term, where and The pore pressure coefficient is determined by the Biot coefficient and Poisson's ratio of the material. The larger the value, the greater the additional stress generated under the same pore pressure gradient.

[0168] Finally, by superimposing the complex potential functions (homogeneous solutions) of each region with the corresponding pore pressure particular solutions (non-homogeneous particular solutions), the complete analytical function expressions for the surrounding rock region and the lining region can be obtained. This superposition process decomposes the complex non-homogeneous problem containing pore pressure terms into the series construction of homogeneous solutions and the separate solving of non-homogeneous particular solutions. This lays the foundation for subsequently transforming the boundary conditions and contact conditions into a closed system of equations with undetermined coefficients. to The boundary and contact conditions will be determined in step 8, while the pore pressure particular solution has been determined by the known water pressure parameters and does not contain any new undetermined coefficients.

[0169] Step 7: Using the water pressure parameters, set the internal water pressure load condition at the inner boundary of the lining. Using the geometric parameters, set the stress continuity condition and displacement continuity condition at the contact surface between the surrounding rock and the lining. The displacement continuity condition incorporates the displacement release coefficient from the construction parameters.

[0170] This step is used to establish mechanical boundary conditions and contact conditions at three key locations in the rock-lining dual-region model, providing a complete equation system for subsequent solution of undetermined coefficients.

[0171] In this embodiment, the internal water pressure load condition is:

[0172] ;

[0173] in, Indicates the radial stress of the lining. Indicates the shear stress of the lining. The imaginary unit, Indicates taking the real part, Represents the complex potential function of the lining The first derivative, Represents the complex potential function of the lining The second derivative, For complex plane coordinates, The imaginary unit, , Represents rectangular coordinate components. Represents the angle in polar coordinates. Represents a complex exponential function. This represents the pore pressure coefficient of the lining. Indicates the pore water pressure in the lining area. This refers to the inner boundary pore pressure in the water pressure parameters. Represents the pore pressure specific solution of the lining region; radial position coordinates at the inner boundary of the lining. , This represents the inner radius of the lining in the geometric parameters;

[0174] The stress continuity condition is:

[0175] ;

[0176] in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. express conjugate, express conjugate, express conjugate, express conjugate, Represents the pore pressure specific solution of the lining area; radial position coordinates at the surrounding rock-lining interface. , Indicates the radius of the contact surface between the surrounding rock and the lining;

[0177] The displacement continuity condition is:

[0178]

[0179] ;

[0180] in, Indicates the radial displacement of the surrounding rock region. This indicates the tangential displacement of the surrounding rock region. This represents the displacement release coefficient in the construction parameters. This represents the shear modulus of the surrounding rock. Indicates the shear modulus of the lining. Represents the Kolosov constant of the surrounding rock. This represents the Kolosov constant for the lining. Indicates the Poisson's ratio of the surrounding rock. Indicates the Poisson's ratio of the lining. Represents complex plane coordinates The conjugate complex coordinates, Represents the complex potential function of the surrounding rock After differentiation, in conjugate complex coordinates Take the value at the given point, then take the conjugate; Represents the complex potential function of the surrounding rock In conjugate complex coordinates Take the value at the given location and take its conjugate; Represents the complex potential function of the lining After differentiation, in conjugate complex coordinates Take the value at the given point, then take the conjugate; Represents the complex potential function of the lining In conjugate complex coordinates Take the value at the given location and take the conjugate.

[0181] Specifically, this step sets conditions in three locations:

[0182] (1) An internal water pressure load condition is set at the inner boundary of the lining. At the inner boundary of the lining ( At this point, the inner wall of the lining directly bears the internal water pressure. Therefore, a surface force boundary condition needs to be established at this boundary, requiring the radial stress at the inner boundary of the lining to be balanced with the internal water pressure. This condition will determine the internal water pressure parameters. The system of equations introduced reflects the direct influence of internal water pressure on the stress state of the lining.

[0183] (2) Stress continuity and displacement continuity conditions are set at the contact surface between the surrounding rock and the lining. At the contact surface between the surrounding rock and the lining ( At this point, the surrounding rock and the lining are in complete contact without separation or relative sliding. Therefore, two sets of continuity conditions must be met simultaneously: the stress continuity condition requires that the stress on both sides of the contact surface be exactly the same, i.e., the stress on the surrounding rock side is equal to the stress on the lining side; the displacement continuity condition requires that the displacement on both sides of the contact surface be exactly the same, i.e., the displacement on the surrounding rock side is equal to the displacement on the lining side. These two sets of conditions together ensure the mechanical coordination between the surrounding rock and the lining at the contact surface, unifying the two areas into a co-forced overall mechanical system.

[0184] (3) Using the displacement release coefficient to set up construction lag conditions characterizing the lag effect of support construction. In actual construction, the lining is not constructed immediately after tunnel excavation; the surrounding rock has already undergone a certain proportion of deformation before the lining is formed. This step introduces the displacement release coefficient into the displacement continuity condition. To describe this construction lag effect, the coefficient represents the proportion of surrounding rock deformation to total deformation before lining construction, and its value typically ranges from 0 to 1. When When the surrounding rock has not undergone any deformation before the lining is installed (immediate support), all deformation of the surrounding rock is borne by the lining; when At this time, it means that the deformation of the surrounding rock has been fully released before the lining is constructed, and the lining only bears the subsequent deformation. The specific value needs to be determined based on the actual construction plan and monitoring data. It appears as a weighting coefficient in the continuous condition of contact surface displacement, so that the actual displacement transmitted from the surrounding rock to the lining is the total displacement. This multiple, thus truly reflecting the impact of construction sequence on the coordinated stress of the surrounding rock and lining.

[0185] The mathematical forms of the above three conditions are all expressed as a combination of the complex potential function constructed in step 6 and the particular solution of the pore pressure. Specifically, the internal water pressure load condition provides one boundary equation, while the stress continuity condition and the displacement continuity condition each provide two equations (complex equations, with the real and imaginary parts corresponding to the normal and tangential components, respectively) at the contact surface. The displacement continuity condition introduces a displacement release coefficient. ,pass Adjust the contribution weight of the surrounding rock lateral displacement without increasing the number of equations.

[0186] Step 8: Substitute the internal water pressure load condition, stress continuity condition, and displacement continuity condition including displacement release coefficient into the analytical function expressions of the pore pressure term in the surrounding rock area and the pore pressure term in the lining area, respectively, to form a closed system of equations with undetermined coefficients and solve it to obtain the analytical function coefficients.

[0187] In this embodiment, the internal water pressure load condition, stress continuity condition, and displacement continuity condition including displacement release coefficient are substituted into the analytical function expressions of the pore pressure term in the surrounding rock region and the pore pressure term in the lining region, respectively. The first three terms are retained to form a closed system of equations with undetermined coefficients and then solved.

[0188] The closed system of equations with undetermined coefficients contains 9 unknown coefficients and 9 equations. The coefficients of the analytic function obtained by solving it are: ,in, Represents the coefficients of an analytic function. , , These represent the first three undetermined coefficients of the complex potential function of the surrounding rock region. , , , , , These represent the first three undetermined coefficients of the complex potential function of the lining region. This indicates the matrix transpose.

[0189] Specifically, this step is used to form and solve a closed system of equations with undetermined coefficients to determine all the unknown coefficients of the complex potential function series expression constructed in step 6. In this embodiment, after substituting the internal water pressure load condition, contact surface stress continuity condition, and displacement continuity condition established in step 7 into the analytical function expressions of the pore pressure terms of the surrounding rock and lining, respectively, the boundary conditions can be transformed into a system of linear algebraic equations with undetermined coefficients by comparing the coefficients of the same power at both ends of the equations.

[0190] Regarding the truncation of series, this embodiment retains the first three terms (up to the level of the surrounding rock region). The lining area will be retained until... Item and The order of the term is chosen based on the following considerations: the first-order term describes the basic stress response under far-field stress and uniform internal pressure, while the third-order term describes the non-uniformity of in-situ stress (lateral pressure coefficient). The asymmetric stress distribution and local stress concentration effect at the contact surface caused by terms not equal to 1 are considered. Retaining the first three terms ensures computational accuracy while controlling the number of unknown coefficients, keeping the size of the equation system within a suitable range for manual programming solutions, thus meeting both engineering accuracy requirements and computational efficiency.

[0191] Under the above truncation scheme, the complex potential function of the surrounding rock region contains three unknown coefficients ( , , The complex potential function of the lining region contains 6 unknown coefficients. , , , , , There are a total of 9 unknown coefficients. The corresponding equations are derived from: the internal water pressure load condition provides one boundary equation on the inner boundary of the lining; the stress continuity condition and the displacement continuity condition each provide one complex equation on the contact surface (the real and imaginary parts correspond to the normal and tangential components, respectively); and the three equations are combined and discussed from different angles. The value of (equivalent to) By matching different powers of the equations, a system of linear algebraic equations is formed, consisting of nine independent equations. This system of equations can be represented in matrix form. ,in This represents the coefficient matrix of a closed system of equations with undetermined coefficients. The constant vector on the right-hand side of the system of equations is used to directly obtain the coefficients of the analytic function using standard linear algebra methods. .

[0192] Once the above nine coefficients are determined, the complex potential function of the surrounding rock and lining will be determined. This means that the solution is completely determined, providing a complete analytical function input for subsequent steps to calculate the stress-displacement distribution across the entire field. Compared to numerical simulations involving tens of thousands of degrees of freedom, this embodiment only requires solving nine unknown coefficients to obtain the full-field solution, thus improving computational efficiency.

[0193] Step 9: Based on the analytical function coefficients and the analytical function expressions of the pore pressure terms in each region, calculate the whole-field radial stress, tangential stress, shear stress, radial displacement, and tangential displacement in the surrounding rock region and the lining region to form the whole-field stress and displacement distribution.

[0194] Specifically, this step is used to calculate the stress and displacement distribution of the surrounding rock and lining throughout the field based on the analytical function coefficients obtained in step 8.

[0195] In this embodiment, the calculation method for the full-field stress and displacement distribution includes steps 91 to 96:

[0196] Step 91: Based on the analytical function coefficients, combined with the far-field principal stress reference value and lateral pressure coefficient in the geostress parameters, and the radius of the rock-lining contact surface in the geometric parameters, calculate the complex potential function of the surrounding rock region and the complex potential function of the lining region.

[0197] The complex potential function of the surrounding rock region is:

[0198] ;

[0199] ;

[0200] The complex potential function of the lining region is:

[0201] ;

[0202] ;

[0203] in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. , This represents the intermediate variable of the far-field stress. , , This represents the reference value of the far-field principal stress in the geostress parameters. This represents the lateral pressure coefficient in the geostress parameters. This represents the radius of the rock-lining contact surface in the geometric parameters. For complex plane coordinates, The imaginary unit, , Represents the rectangular coordinate components.

[0204] Specifically, step 91 substitutes the nine analytical function coefficients obtained in step 8 into the complex potential function expressions for the surrounding rock and lining, and superimposes the initial term generated by the far-field stress (derived from the far-field principal stress reference value). and lateral pressure coefficient jointly determined and ), thus obtaining the complete complex potential function for each region. The aforementioned complex potential function contains all the information about the effects of geostress, pore water pressure, and the contact transmission between the surrounding rock and the lining.

[0205] Step 92: Based on the total stress function of the surrounding rock area Calculate the stress components of the surrounding rock region in rectangular coordinates:

[0206] ;

[0207] ;

[0208] ;

[0209] in, , This represents the normal stress components in rectangular coordinates of the surrounding rock region. This represents the shear stress components in the surrounding rock region. This represents the total stress function in the surrounding rock region. , This represents the stress function decomposition term in the surrounding rock region.

[0210] Step 93: Based on the total stress function of the lining area Calculate the stress components of the lining area in rectangular coordinates:

[0211] ;

[0212] ;

[0213] ;

[0214] in, , This represents the normal stress components in rectangular coordinates of the lining area. This represents the shear stress components in the lining area. This represents the total stress function in the lining area. , This represents the stress function decomposition term in the lining area.

[0215] Specifically, steps 92 and 93 are based on the total stress function of each region. Calculate the stress components in rectangular coordinates. Wherein, The homogeneous biharmonic equation in step 4 The solution corresponds to the stress contribution when pore water pressure is not considered; The particular solution of pore pressure constructed in step 6 corresponds to the additional stress contribution caused by pore water pressure. The total stress function... right and By taking the second-order partial derivatives, the normal stress components are obtained. , and shear stress components The above operations were performed independently in the surrounding rock region and the lining region, respectively, to obtain three stress components in rectangular coordinates for each region.

[0216] Step 94: Calculate the displacement components of the surrounding rock region in rectangular coordinates based on the complex potential function of the surrounding rock region.

[0217] ;

[0218] in, This represents the shear modulus of the surrounding rock. , This represents the displacement components in rectangular coordinates of the surrounding rock region. This represents the Poisson's ratio of the surrounding rock.

[0219] Step 95: Calculate the displacement components of the lining region in rectangular coordinates based on the complex potential function of the lining region.

[0220] ;

[0221] in, Indicates the shear modulus of the lining. , This represents the displacement components of the lining area in rectangular coordinates. This indicates the Poisson's ratio of the lining.

[0222] Specifically, steps 94 and 95 calculate the displacement components in rectangular coordinates based on the complex potential function of each region. In the complex variable function method of elasticity, the complex potential function... The displacement field is directly determined by the stress function: the components of normal stress and shear stress are determined by the stress function. The partial derivative is obtained, while the displacement component ( , Then, by the complex potential function With stress function decomposition terms , The partial derivatives are combined to express the complex potential function. The above formula expresses the complex potential function. and Substitute the values ​​into the displacement calculation formulas for the surrounding rock and lining respectively, and combine them with the shear modulus of the materials in each region. Compared to Poisson The displacement components of the surrounding rock and lining in rectangular coordinates were calculated and denoted as follows: , and , .

[0223] Step 96: Convert the stress components in rectangular coordinates. , , , , , After coordinate transformation, the full-field radial stress, tangential stress, and shear stress in the surrounding rock region and lining region are obtained; the displacement components in rectangular coordinates are then transformed. , , , After coordinate transformation, the full-field radial and tangential displacements of the surrounding rock area and the lining area are obtained.

[0224] Specifically, step 96 converts the stress and displacement components in rectangular coordinates to polar coordinates using a standard coordinate transformation formula, obtaining the components of the surrounding rock region and the lining region at any radius across the entire field. and angle The radial stress, tangential stress, shear stress, radial displacement, and tangential displacement at the location are given. The stress and displacement components in polar coordinates directly correspond to the circumferential force and radial deformation that are of concern in the design of circular tunnels, facilitating comparison with engineering specifications and design allowable values.

[0225] In the above process, only 9 undetermined coefficients are needed to obtain the analytical solution for the entire field. Once the coefficients are determined, the stress and displacement at any radius and angle can be quickly calculated by directly substituting them into the analytical expression, avoiding the time consumption of repeated modeling and iterative calculations. By determining the stress and displacement distribution of the surrounding rock and lining throughout the field, complete mechanical response data is provided for step 10 to extract risk identification indicators.

[0226] This embodiment is based on the following example parameters: , , , , , , , , , , External water head is taken separately , , , , The calculated stress distribution curve is as follows: Figures 4 to 6 As shown.

[0227] Please see Figure 4 , Figure 4 For lining the inner boundary ( Circumferential stress at point ) varies with angle The graph shows the distribution curve. The horizontal axis represents angle (degrees), and the vertical axis represents circumferential stress (MPa). From... Figure 4 It can be seen that the circumferential stress at the inner boundary of the lining is all compressive stress (negative value). The stress magnitude varies at different angular locations, reflecting the non-uniformity of ground stress (lateral pressure coefficient). The influence of circumferential compressive stress on the lining. The maximum value of circumferential compressive stress occurs at approximately 90° (i.e., on both sides of the tunnel), which is the most unfavorable stress orientation of the inner boundary of the lining.

[0228] Please see Figure 5 , Figure 5 The outer boundary of the lining (i.e., the contact surface between the surrounding rock and the lining) Circumferential stress at point ) varies with angle A graph showing the distribution. (Compared to...) Figure 4 In contrast, the overall circumferential compressive stress at the outer boundary of the lining is slightly lower than that at the inner boundary, but its trend with angle is basically the same as that at the inner boundary, with stress extrema also appearing at approximately 90°. These results indicate that stress transfer at the contact surface has a clear directionality, and identifying the critical azimuth angle is instructive for determining the reinforcement range of the contact surface.

[0229] Please see Figure 6 , Figure 6 Vertical direction ( (Direction) Radial stress varies with radial position Distribution curve. The horizontal axis in the graph represents the dimensionless radial position (with the inner radius of the lining). (Normalized), the vertical axis represents radial stress (unit: MPa); the vertical dashed line marks the location of the lining-surrounding rock contact surface ( The left side area is lining ( The area on the right is surrounding rock ( ).Depend on Figure 6 It can be seen that the radial stress is in equilibrium with the internal water pressure at the inner boundary of the lining, and gradually increases from the inside to the outside. After passing through the contact surface and entering the surrounding rock area, the radial stress continues to increase and gradually approaches the stress value at the far-field location, which is consistent with the basic law of stress distribution in the surrounding rock of deeply buried tunnels. This curve verifies the continuity and rationality of the stress field calculated in step 9 in the radial direction, and also reflects the stress coordination relationship between the surrounding rock and the lining at the contact surface.

[0230] Step 10: Extract risk identification indicators based on the full-field stress and displacement distribution, compare the risk identification indicators with the risk discrimination parameters, and output the high external water risk area identification results and external water sensitivity evaluation results.

[0231] In this embodiment, step 10 specifically includes steps 101 to 104:

[0232] Step 101: Determine the maximum tangential stress index and corresponding critical azimuth angle at the inner boundary of the lining based on the tangential stress distribution at the inner boundary of the lining.

[0233] ;

[0234] ;

[0235] in, This indicates the maximum tangential stress index at the inner boundary of the lining. Indicates the angle at the inner boundary of the lining. Tangential stress at the location, radial position coordinates at the inner boundary of the lining. , This represents the inner radius of the lining in the geometric parameters. Indicates the angle Take the maximum value. Indicates the danger azimuth. This represents the angle at which the function reaches its maximum value. Values.

[0236] Specifically, the inner boundary of the lining is the location that directly bears the internal water pressure and has the highest risk of fracturing. The tangential stress distribution at this location determines whether the lining will experience fracturing failure. This step extracts the inner boundary of the lining based on the full-field tangential stress distribution of the lining area obtained in step 96. (at different angles) Tangential stress Search for the maximum value from it. and their corresponding angles . This reflects the maximum stress level of the lining at the most unfavorable location. This indicates the specific location where the maximum stress occurs, providing a clear directional basis for determining the reinforcement range in engineering. Because the stress field of the surrounding rock in deeply buried tunnels is usually non-uniform (lateral pressure coefficient...),... The lining stress varies at different angles. The identification can accurately capture the most unfavorable response orientation caused by this non-uniformity.

[0237] Step 102: The maximum tangential stress at the inner boundary of the lining... Compared with the lining compressive strength limit in the risk discrimination parameters Compare; when At that time, determine the dangerous azimuth angle. There is a risk of fracturing at the lining boundary; otherwise, it is determined that there is no risk of fracturing at the inner boundary of the lining.

[0238] Specifically, when Exceed When this occurs, it indicates that the stress at that angle has exceeded the compressive bearing capacity of the material, thus determining the critical azimuth angle. There is a risk of hydraulic fracturing in this area; therefore, targeted reinforcement or depressurization measures should be implemented in this location during the project. Conversely, when... No more than At that time, it was determined that there was no risk of cracking at the inner boundary of the lining under the current working conditions.

[0239] Step 103: According to different external water head The maximum tangential stress at the inner boundary of the lining under the specified conditions Rate of change determines external water sensitivity index :

[0240] ;

[0241] in, and This indicates two different external water head values. and This represents the maximum tangential stress at the inner boundary of the lining under the corresponding external water head.

[0242] Specifically, based on the determination of a high external water head condition in step 2, two different external water head values ​​are selected, and the corresponding maximum tangential stress is calculated respectively. The relationship between the two is defined as an external water sensitivity index. The larger this index is, the more sensitive the lining is to changes in external water head; that is, even a small increase in external water pressure can cause a significant increase in lining stress.

[0243] Step 104: The external water sensitivity index Compared with the external water sensitivity threshold in the risk discrimination parameters Comparison; when the external water sensitivity index Exceeding the aforementioned external water sensitivity threshold If the condition is positive, it is determined to be a water-sensitive condition; otherwise, it is determined to be a non-water-sensitive condition.

[0244] Specifically, when Exceed If the project is deemed to be in a water-sensitive condition, it is recommended to impose stricter restrictions on the range of operating water level changes during the design phase, or to reserve a higher safety margin in the lining structure design; otherwise, it is deemed to be in a non-water-sensitive condition and can be handled according to conventional design methods.

[0245] In summary, the high external water risk identification method for deeply buried lined tunnels provided in this embodiment establishes a dual-region plane strain model for co-solving the surrounding rock and lining regions. It directly solves the non-homogeneous governing equations containing pore pressure terms using the complex variable method, rapidly obtaining the stress-displacement distribution across the entire field of the surrounding rock and lining without requiring extensive numerical iterations. This significantly improves the efficiency of multi-condition screening and parameter sensitivity analysis under high external water conditions. Furthermore, this embodiment introduces pore water pressure as an internal field variable into the constitutive relationship of the surrounding rock and lining. It constructs complex potential functions and pore pressure particular solutions for each region by combining the radial distribution function of pore water pressure under the quasi-steady-state seepage assumption, and utilizes the internal water pressure load... The conditions, contact surface stress continuity and displacement continuity conditions, and displacement release coefficient form a closed system of equations for solution, which truly reflects the mechanism of change of effective stress state by pore water pressure field and the synergistic force relationship between the two regions, effectively improving the accuracy of risk identification and making the calculation results more consistent with the actual impact of construction lag effect. Furthermore, this embodiment judges the fracturing risk by extracting the maximum tangential stress index of the inner boundary of the lining and the corresponding dangerous azimuth angle, and evaluates the external water sensitivity based on the rate of change of maximum tangential stress under different external water heads, providing a clear theoretical basis for lining crack resistance design, precise reinforcement of dangerous parts and operation water level control.

[0246] Based on the above technical solution, this embodiment also proposes a high external water risk identification system for deeply buried lined tunnels, used to implement the high external water risk identification method for deeply buried lined tunnels as described in the embodiment. Please refer to [link to relevant documentation]. Figure 7 The system includes:

[0247] The parameter acquisition module is used to collect the input parameters required for risk identification of deeply buried lined tunnels. The input parameters include: geometric parameters, material parameters, ground stress parameters, water pressure parameters, construction parameters, and risk discrimination parameters.

[0248] The operating condition determination module is used to determine whether the current operating condition is a high external water condition based on the water pressure parameters. If the condition is determined to be a high external water condition, the subsequent steps are performed.

[0249] The model building module is used to establish a dual-region plane strain model for collaborative solution of the surrounding rock region and the lining region using the geometric parameters.

[0250] The governing equation construction module is used to utilize the material parameters and geostress parameters, based on the pore elasticity theory, and introduce pore water pressure as an internal field variable into the constitutive relations of the surrounding rock and the lining, respectively, to construct non-homogeneous governing equations with pore pressure terms in the surrounding rock region and non-homogeneous governing equations with pore pressure terms in the lining region in the dual-region plane strain model.

[0251] The pore pressure distribution establishment module is used to establish the radial distribution function of pore water pressure in the surrounding rock area and the radial distribution function of pore water pressure in the lining area under the quasi-steady-state seepage assumption using the geometric parameters and water pressure parameters.

[0252] The analytical function construction module is used to construct the complex potential function of the surrounding rock region and the complex potential function of the lining region based on the non-homogeneous governing equations of the pore pressure term in the surrounding rock region and the non-homogeneous governing equations of the pore pressure term in the lining region, respectively. Based on the radial distribution function of pore water pressure in the surrounding rock region and the radial distribution function of pore water pressure in the lining region, it constructs the particular solution of pore pressure in the surrounding rock region and the particular solution of pore pressure in the lining region, respectively. The complex potential function of each region is superimposed with the corresponding particular solution of pore pressure to form the analytical function expression of the pore pressure term in each region.

[0253] The condition setting module is used to set internal water pressure load conditions at the inner boundary of the lining using the water pressure parameters, and to set stress continuity conditions and displacement continuity conditions at the contact surface between the surrounding rock and the lining using the geometric parameters. The displacement continuity condition incorporates the displacement release coefficient from the construction parameters.

[0254] The equation solving module is used to substitute the internal water pressure load condition, stress continuity condition, and displacement continuity condition including displacement release coefficient into the analytical function expression of the pore pressure term in the surrounding rock area and the analytical function expression of the pore pressure term in the lining area, respectively, to form a closed equation system with undetermined coefficients and solve it to obtain the analytical function coefficients.

[0255] The stress-displacement calculation module is used to calculate the whole-field radial stress, tangential stress, shear stress, radial displacement, and tangential displacement of the surrounding rock area and the lining area based on the analytical function coefficients and the analytical function expression of the pore pressure term in each region, thus forming the whole-field stress and displacement distribution;

[0256] The risk identification module is used to extract risk identification indicators based on the stress and displacement distribution across the entire field, compare the risk identification indicators with the risk discrimination parameters, and output the identification results of high external water risk areas and the evaluation results of external water sensitivity.

[0257] It is understood that the high external water risk identification system for deep-buried lined tunnels described in this embodiment is a system used to implement the high external water risk identification method for deep-buried lined tunnels described in the embodiment. As the system disclosed in the embodiment corresponds to the method disclosed in the embodiment, the description is relatively simple. For relevant parts, please refer to the description of the method. It will not be repeated here.

Claims

1. A method for identifying high external water risk in deeply buried lined tunnels, characterized in that, The method includes: Step 1: Collect the input parameters required for risk identification of deeply buried lined tunnels. The input parameters include: geometric parameters, material parameters, ground stress parameters, water pressure parameters, construction parameters, and risk discrimination parameters. Step 2: Determine whether the current operating condition is a high external water condition based on the water pressure parameters. If it is, proceed to the next step. Step 3: Use the geometric parameters to establish a dual-region plane strain model for the coordinated solution of the surrounding rock region and the lining region; Step 4: Using the material parameters and geostress parameters, based on the pore elasticity theory, pore water pressure is introduced as an internal field variable into the constitutive relations of the surrounding rock and the lining, respectively. In the dual-region plane strain model, non-homogeneous control equations with pore pressure terms in the surrounding rock region and non-homogeneous control equations with pore pressure terms in the lining region are constructed, respectively. Step 5: Using the geometric parameters and water pressure parameters, establish the radial distribution function of pore water pressure in the surrounding rock area and the radial distribution function of pore water pressure in the lining area under the quasi-steady-state seepage assumption, respectively. Step 6: Based on the non-homogeneous governing equations of the pore pressure terms in the surrounding rock region and the pore pressure terms in the lining region, construct the complex potential function of the surrounding rock region and the complex potential function of the lining region, respectively. Based on the radial distribution function of pore water pressure in the surrounding rock region and the radial distribution function of pore water pressure in the lining region, construct the particular solution of pore pressure in the surrounding rock region and the particular solution of pore pressure in the lining region, respectively. Superimpose the complex potential function of each region with the corresponding particular solution of pore pressure to form the analytical function expression of the pore pressure terms in each region. Step 7: Using the water pressure parameters, set the internal water pressure load condition at the inner boundary of the lining; using the geometric parameters, set the stress continuity condition and displacement continuity condition at the contact surface between the surrounding rock and the lining; the displacement continuity condition introduces the displacement release coefficient from the construction parameters. Step 8: Substitute the internal water pressure load condition, stress continuity condition, and displacement continuity condition including displacement release coefficient into the analytical function expression of the pore pressure term in the surrounding rock area and the analytical function expression of the pore pressure term in the lining area, respectively, to form a closed system of equations with undetermined coefficients and solve it to obtain the analytical function coefficients. Step 9: Based on the analytical function coefficients and the analytical function expressions of the pore pressure terms in each region, calculate the whole-field radial stress, tangential stress, shear stress, radial displacement, and tangential displacement in the surrounding rock region and the lining region to form the whole-field stress and displacement distribution; Step 10: Extract risk identification indicators based on the full-field stress and displacement distribution, compare the risk identification indicators with the risk discrimination parameters, and output the high external water risk area identification results and external water sensitivity evaluation results.

2. The method for identifying high external water risk in deeply buried lined tunnels according to claim 1, characterized in that, Step 2 involves determining whether the current operating condition is a high external water condition based on the water pressure parameters. Specifically, this includes: Calculate the head difference based on the external water head and internal water head in the aforementioned water pressure parameters: ,in, Indicates the difference in water head. Indicates external water head. Indicates the internal water head; Calculate the pore pressure difference based on the far-field pore pressure and the inner boundary pore pressure in the aforementioned water pressure parameters: ,in, Indicates the orifice pressure difference. Indicates far-field pore pressure, Indicates the pore pressure at the inner boundary; The high external water condition meets at least one of the following conditions: The head difference is positive, meaning the external water head is higher than the internal water head. The pore pressure difference is positive, meaning that the far-field pore pressure is higher than the inner boundary pore pressure. Under maintenance, venting, or low internal water pressure conditions, the contribution of the external water pressure calculated based on the head difference or pore pressure difference to the change of the target stress displacement index reaches a preset threshold. The target stress displacement index is the maximum tangential stress of the inner boundary of the lining or the radial displacement of the inner boundary of the lining.

3. The method for identifying high external water risk in deeply buried lined tunnels according to claim 1, characterized in that, In step 4, the non-homogeneous governing equation for the pore pressure term in the surrounding rock region is: ； The non-homogeneous governing equation for the lining region, including the pore pressure term, is: ； in, , , , , , , , , Represents the Biot coefficient of the surrounding rock. Indicates the Poisson's ratio of the surrounding rock. Indicates the Biot coefficient of the lining. Indicates the Poisson's ratio of the lining. This represents the pore pressure coefficient of the surrounding rock. This represents the pore pressure coefficient of the lining. Indicates the pore water pressure in the surrounding rock region. Indicates the pore water pressure in the lining area. For the Laplace operator, For a bitone operator, This represents the total stress function in the surrounding rock region. This represents the total stress function in the lining area. , This represents the stress function decomposition terms in the surrounding rock region. , This represents the stress function decomposition term in the lining area.

4. The method for identifying high external water risk in deeply buried lined tunnels according to claim 1, characterized in that, In step 5, the radial distribution function of pore water pressure in the surrounding rock region is: ； The radial distribution function of pore water pressure in the lining region is: ； in, Indicates the pore water pressure in the surrounding rock region. Indicates the pore water pressure in the lining area. , , These represent the inner radius of the lining, the radius of the contact surface between the surrounding rock and the lining, and the radius of the far-field outer boundary, respectively, in the geometric parameters. , , , These represent the far-field pore pressure, inner boundary pore pressure, surrounding rock side contact pore pressure, and lining side contact pore pressure, respectively. Indicates radial position coordinates, It represents the natural logarithm.

5. The method for identifying high external water risk in deeply buried lined tunnels according to claim 4, characterized in that, In step 6, the complex potential function of the surrounding rock region is expressed using a Taylor series as follows: ， ； The complex potential function of the lining region is expressed using Laurent series: ， ； in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. , , , , , Denotes the undetermined complex potential coefficient. Represents the order of a series. For complex plane coordinates, The imaginary unit, , Represents rectangular coordinate components; The pore pressure specific solution of the surrounding rock region for: ； The pore pressure particular solution of the lining region for: ； in, This represents the pore pressure coefficient of the surrounding rock. This represents the pore pressure coefficient of the lining. This represents a constant term.

6. The method for identifying high external water risk in deeply buried lined tunnels according to claim 1, characterized in that, In step 7, the internal water pressure load condition is: ； in, Indicates the radial stress of the lining. Indicates the shear stress of the lining. The imaginary unit, Indicates taking the real part, Represents the complex potential function of the lining The first derivative, Represents the complex potential function of the lining The second derivative, For complex plane coordinates, The imaginary unit, , Represents rectangular coordinate components. Represents the angle in polar coordinates. Represents a complex exponential function. This represents the pore pressure coefficient of the lining. Indicates the pore water pressure in the lining area. This refers to the inner boundary pore pressure in the water pressure parameters. Represents the pore pressure specific solution of the lining region; radial position coordinates at the inner boundary of the lining. , This represents the inner radius of the lining in the geometric parameters; The stress continuity condition is: ； in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. express conjugate, express conjugate, express conjugate, express conjugate, Represents the pore pressure specific solution of the lining area; radial position coordinates at the surrounding rock-lining interface. , Indicates the radius of the contact surface between the surrounding rock and the lining; The displacement continuity condition is: ； in, Indicates the radial displacement of the surrounding rock region. This indicates the tangential displacement of the surrounding rock region. This represents the displacement release coefficient in the construction parameters. This represents the shear modulus of the surrounding rock. Indicates the shear modulus of the lining. Represents the Kolosov constant of the surrounding rock. This represents the Kolosov constant for the lining. Indicates the Poisson's ratio of the surrounding rock. Indicates the Poisson's ratio of the lining. Represents complex plane coordinates The conjugate complex coordinates, Represents the complex potential function of the surrounding rock After differentiation, in conjugate complex coordinates Take the value at the given point, then take the conjugate; Represents the complex potential function of the surrounding rock In conjugate complex coordinates Take the value at the given location and take its conjugate; Represents the complex potential function of the lining After differentiation, in conjugate complex coordinates Take the value at the given point, then take the conjugate; Represents the complex potential function of the lining In conjugate complex coordinates Take the value at the given location and take the conjugate.

7. The method for identifying high external water risk in deeply buried lined tunnels according to claim 1, characterized in that, In step 8, the internal water pressure load condition, stress continuity condition, and displacement continuity condition including displacement release coefficient are substituted into the analytical function expression of the pore pressure term in the surrounding rock area and the analytical function expression of the pore pressure term in the lining area, respectively. The first three terms are retained to form a closed system of equations with undetermined coefficients and then solved. The closed system of equations with undetermined coefficients contains 9 unknown coefficients and 9 equations. The coefficients of the analytic function obtained by solving it are: ,in, Represents the coefficients of an analytic function. , , These represent the first three undetermined coefficients of the complex potential function of the surrounding rock region. , , , , , These represent the first three undetermined coefficients of the complex potential function of the lining region. This indicates the matrix transpose.

8. The method for identifying high external water risk in deeply buried lined tunnels according to claim 7, characterized in that, In step 9, the calculation method for the overall stress and displacement distribution includes: Step 91: Based on the analytical function coefficients, combined with the far-field principal stress reference value and lateral pressure coefficient in the geostress parameters, and the radius of the rock-lining contact surface in the geometric parameters, calculate the complex potential function of the surrounding rock region and the complex potential function of the lining region. The complex potential function of the surrounding rock region is: ； ； The complex potential function of the lining region is: ； ； in, , These represent two complex potential functions of the surrounding rock region. , These represent two complex potential functions of the lining region. , This represents the intermediate variable of the far-field stress. , , This represents the reference value of the far-field principal stress in the geostress parameters. This represents the lateral pressure coefficient in the geostress parameters. This represents the radius of the rock-lining contact surface in the geometric parameters. For complex plane coordinates, The imaginary unit, , Represents rectangular coordinate components; Step 92: Based on the total stress function of the surrounding rock area Calculate the stress components of the surrounding rock region in rectangular coordinates: ； ； ； in, , This represents the normal stress components in rectangular coordinates of the surrounding rock region. This represents the shear stress components in the surrounding rock region. This represents the total stress function in the surrounding rock region. , Represents the stress function decomposition terms in the surrounding rock region; Step 93: Based on the total stress function of the lining area Calculate the stress components of the lining area in rectangular coordinates: ； ； ； in, , This represents the normal stress components in rectangular coordinates of the lining area. This represents the shear stress components in the lining area. This represents the total stress function in the lining area. , This represents the stress function decomposition terms in the lining area; Step 94: Calculate the displacement components of the surrounding rock region in rectangular coordinates based on the complex potential function of the surrounding rock region. ； in, This represents the shear modulus of the surrounding rock. , This represents the displacement components in rectangular coordinates of the surrounding rock region. Indicates the Poisson's ratio of the surrounding rock; Step 95: Calculate the displacement components of the lining region in rectangular coordinates based on the complex potential function of the lining region. ； in, Indicates the shear modulus of the lining. , This represents the displacement components of the lining area in rectangular coordinates. Indicates the Poisson's ratio of the lining; Step 96: Convert the stress components in rectangular coordinates. , , , , , After coordinate transformation, the full-field radial stress, tangential stress, and shear stress in the surrounding rock region and lining region are obtained; the displacement components in rectangular coordinates are then transformed. , , , After coordinate transformation, the full-field radial and tangential displacements of the surrounding rock area and the lining area are obtained.

9. The method for identifying high external water risk in deeply buried lined tunnels according to claim 1, characterized in that, Step 10 specifically includes: Step 101: Determine the maximum tangential stress index and corresponding critical azimuth angle at the inner boundary of the lining based on the tangential stress distribution at the inner boundary of the lining. ； ； in, This indicates the maximum tangential stress index at the inner boundary of the lining. Indicates the angle at the inner boundary of the lining. Tangential stress at the location, radial position coordinates at the inner boundary of the lining. , This represents the inner radius of the lining in the geometric parameters. Indicates the angle Take the maximum value. Indicates the danger azimuth. This represents the angle at which the function reaches its maximum value. Values; Step 102: The maximum tangential stress at the inner boundary of the lining... Compared with the lining compressive strength limit in the risk discrimination parameters Compare; when At that time, determine the dangerous azimuth angle. There is a risk of fracturing at the location; otherwise, it is determined that there is no risk of fracturing at the inner boundary of the lining. Step 103: According to different external water head The maximum tangential stress at the inner boundary of the lining under the specified conditions Rate of change determines external water sensitivity index : ； in, and This indicates two different external water head values. and This represents the maximum tangential stress at the inner boundary of the lining under the corresponding external water head. Step 104: The external water sensitivity index Compared with the external water sensitivity threshold in the risk discrimination parameters Comparison; when the external water sensitivity index Exceeding the aforementioned external water sensitivity threshold If the condition is positive, it is determined to be a water-sensitive condition; otherwise, it is determined to be a non-water-sensitive condition.

10. A high external water risk identification system for deeply buried lined tunnels, characterized in that, For implementing the high external water risk identification method for deeply buried lined tunnels as described in any one of claims 1 to 9, the system comprises: The parameter acquisition module is used to collect the input parameters required for risk identification of deeply buried lined tunnels. The input parameters include: geometric parameters, material parameters, ground stress parameters, water pressure parameters, construction parameters, and risk discrimination parameters. The operating condition determination module is used to determine whether the current operating condition is a high external water condition based on the water pressure parameters. If the condition is determined to be a high external water condition, the subsequent steps are performed. The model building module is used to establish a dual-region plane strain model for collaborative solution of the surrounding rock region and the lining region using the geometric parameters. The governing equation construction module is used to utilize the material parameters and geostress parameters, based on the pore elasticity theory, and introduce pore water pressure as an internal field variable into the constitutive relations of the surrounding rock and the lining, respectively, to construct non-homogeneous governing equations with pore pressure terms in the surrounding rock region and non-homogeneous governing equations with pore pressure terms in the lining region in the dual-region plane strain model. The pore pressure distribution establishment module is used to establish the radial distribution function of pore water pressure in the surrounding rock area and the radial distribution function of pore water pressure in the lining area under the quasi-steady-state seepage assumption using the geometric parameters and water pressure parameters. The analytical function construction module is used to construct the complex potential function of the surrounding rock region and the complex potential function of the lining region based on the non-homogeneous governing equations of the pore pressure term in the surrounding rock region and the non-homogeneous governing equations of the pore pressure term in the lining region, respectively. Based on the radial distribution function of pore water pressure in the surrounding rock region and the radial distribution function of pore water pressure in the lining region, it constructs the particular solution of pore pressure in the surrounding rock region and the particular solution of pore pressure in the lining region, respectively. The complex potential function of each region is superimposed with the corresponding particular solution of pore pressure to form the analytical function expression of the pore pressure term in each region. The condition setting module is used to set internal water pressure load conditions at the inner boundary of the lining using the water pressure parameters, and to set stress continuity conditions and displacement continuity conditions at the contact surface between the surrounding rock and the lining using the geometric parameters. The displacement continuity condition incorporates the displacement release coefficient from the construction parameters. The equation solving module is used to substitute the internal water pressure load condition, stress continuity condition, and displacement continuity condition including displacement release coefficient into the analytical function expression of the pore pressure term in the surrounding rock area and the analytical function expression of the pore pressure term in the lining area, respectively, to form a closed equation system with undetermined coefficients and solve it to obtain the analytical function coefficients. The stress-displacement calculation module is used to calculate the whole-field radial stress, tangential stress, shear stress, radial displacement, and tangential displacement of the surrounding rock area and the lining area based on the analytical function coefficients and the analytical function expression of the pore pressure term in each region, thus forming the whole-field stress and displacement distribution; The risk identification module is used to extract risk identification indicators based on the stress and displacement distribution across the entire field, compare the risk identification indicators with the risk discrimination parameters, and output the identification results of high external water risk areas and the evaluation results of external water sensitivity.

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