A method and equipment for analyzing seepage field in cracked linings of water-rich strata

Abstract

This invention discloses a method and equipment for analyzing the seepage field in the lining of cracked water-rich strata, belonging to the field of tunnel engineering seepage analysis technology. It addresses the technical problems in existing tunnel engineering seepage analysis, such as the difficulty in directly and analytically modeling complex cracks, the poor practicality of three-dimensional numerical simulation methods, and the insufficient consideration of the mutual interference between the tunnel and cracks. The method includes: performing equivalent seepage calculations on the equivalent circular drainage holes under the relevant total seepage flow; placing the equivalent circular drainage holes within the tunnel lining boundary, with the distance between the equivalent circular drainage holes and the tunnel lining boundary approaching zero; transforming the horseshoe-shaped non-circular boundary of the tunnel into a regular unit circle boundary under conformal mapping; and performing alternating two-dimensional seepage iterations on the excess hydraulic gradient generated by the equivalent circular drainage holes on the tunnel and the excess water head generated by the tunnel on the equivalent circular drainage holes under multiple connected domains to obtain the analytical results of the seepage field.

Description

Technical Field

[0001] This application relates to the field of seepage analysis technology in tunnel engineering, and in particular to a method and equipment for analyzing the seepage field of cracked lining in water-rich strata. Background Technology

[0002] During the construction and operation of tunnel projects in water-rich strata, the lining is affected by multiple factors such as geological load and structural deformation, which can easily lead to cracks of different shapes. The dynamic changes in external water pressure caused by crack seepage are the core external factors affecting the stability of the tunnel structure and are directly related to the safe operation of the tunnel project.

[0003] In actual engineering, the lining cracks have various forms, including straight cracks, oblique cracks, and mesh cracks. Their size parameters (width, depth, length) vary greatly, and their permeability characteristics (permeability, drainage pressure) are complex and variable. They are typical irregular and unquantifiable permeability boundaries, which cannot be directly incorporated into the seepage field control equation for analytical solution. This has become the core technical bottleneck in the seepage analysis of cracked linings.

[0004] There are two main approaches to analyzing the seepage field in cracked linings in the existing technology, but both have obvious drawbacks: one is to directly use three-dimensional numerical simulation analysis, which is cumbersome to solve, has a huge amount of computation, and lacks the support of theoretical analytical models. The universality and accuracy of the calculation results are difficult to guarantee, and the cost of engineering application is high. The other is to oversimplify the cracks, ignore the actual seepage characteristics of the cracks, and only make simple equivalents in terms of geometric morphology. This leads to a serious disconnect between the established theoretical model and the actual engineering situation, and the analysis results cannot effectively guide engineering practice.

[0005] Meanwhile, horseshoe-shaped and other non-circular cross-section linings are widely used in tunnel engineering. Their complex cross-sectional shape further increases the difficulty of analytical modeling of the seepage field. Existing analysis methods have not achieved accurate analysis of the seepage field of "complex cracks + non-circular cross-section" linings. They cannot provide reliable theoretical data support for the analysis of the disaster mechanism of cracked linings in water-rich strata tunnels and the design of protection and reinforcement. It is difficult to accurately conduct effective data analysis on the seepage field of water-rich strata tunnel engineering. Summary of the Invention

[0006] This application provides a method and equipment for analyzing the seepage field of cracked lining in water-rich strata, which is used to solve the following technical problems: In the existing tunnel engineering seepage analysis, complex cracks are difficult to model directly analytically, and the three-dimensional numerical simulation method is also less practical, and the mutual interference between the tunnel and the crack has not been fully considered.

[0007] The embodiments of this application adopt the following technical solutions: On one hand, this application provides a method for analyzing the seepage field of a cracked lining in a water-rich stratum, including: based on the total flow rate of the entire actual pressurized crack, performing equivalent seepage calculations on equivalent circular drainage holes under the relevant total seepage flow rate to obtain the equivalent hydraulic radius of the equivalent circular drainage holes after crack equivalent transformation; setting the equivalent circular drainage holes in the tunnel lining boundary, with the distance between the equivalent circular drainage holes and the tunnel lining boundary approaching zero, and obtaining the distribution location of the circular drainage holes; based on the continuity of groundwater seepage, establishing a two-dimensional stable seepage control equation for the tunnel lining boundary and determining the boundary conditions; and under the condition that the equivalent hydraulic radius and the distribution location of the circular drainage holes are satisfied... The horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under conformal mapping to obtain a planar unit circle. Based on the single connected domain of the equivalent hole of the crack and the single connected domain of the tunnel under the planar unit circle, and based on the two-dimensional stable seepage control equation and boundary conditions, the redundant hydraulic gradient generated by the equivalent circular drainage hole on the tunnel and the redundant water head generated by the tunnel on the equivalent circular drainage hole are subjected to two-dimensional seepage alternating iteration under multiple connected domains to obtain the hydraulic disturbance of the tunnel and the equivalent circular drainage hole after each alternating iteration correction. Based on the corrected hydraulic disturbance after each alternating iteration correction and the initial hydraulic, the analytical results of the seepage field under the mutual influence of the tunnel and the equivalent circular drainage hole are calculated and obtained.

[0008] This application addresses the core problem of complex cracks' inability to be analytically modeled by equating the complex seepage behavior of lining cracks to the regular drainage behavior of near-circular drainage holes around the lining and providing a quantitative calculation formula for the equivalent hydraulic radius. Based on this, the Schwartz alternation method is used to solve the seepage problem in multiple connected domains formed by the tunnel and the equivalent drainage holes, accurately considering their mutual interference. Simultaneously, the conformal mapping method is combined to transform the complex boundary of the horseshoe-shaped non-circular cross-section into a regular unit circle boundary. Finally, a two-dimensional analytical model of the seepage field of the non-circular cracked lining is established and solved, achieving accurate and efficient analysis of the seepage field and external water pressure distribution law of cracked linings in water-rich strata. This provides reliable theoretical data support for the analysis of the disaster mechanism and the design of protection and reinforcement of cracked linings in water-rich strata tunnels, filling a gap in existing technologies.

[0009] In one feasible implementation, based on the total flow rate of the entire actual pressurized fracture, a permeability equivalence calculation is performed on the equivalent circular drainage hole under the relevant total seepage flow rate to obtain the equivalent hydraulic radius of the equivalent circular drainage hole after the fracture equivalence transformation. Specifically, this includes: based on the principle of permeability equivalence, performing equivalent processing on the actual pressurized fracture for key permeability parameters such as seepage flow rate per unit length, seepage velocity, and drainage pressure to obtain the equivalent circular drainage hole; wherein, the equivalent circular drainage hole and the overall permeability behavior of the actual pressurized fracture are equivalently matched; based on gravity acceleration and tunnel cracking lining... The seepage flow rate per unit length of the actual pressurized fracture is obtained by considering the fracture aperture, water kinematic viscosity coefficient, head difference between the two ends of the fracture, and lining thickness. The total flow rate of the entire fracture is then obtained based on the longitudinal length of the fracture along the tunnel. The total seepage flow rate of the equivalent circular drainage hole is determined based on the Hagen–Poiseuille law, since the seepage in the equivalent circular drainage hole is laminar flow in a circular pipe. Finally, the equivalent hydraulic radius of the equivalent circular drainage hole after the fracture is equivalently transformed is obtained by performing a simultaneous equation between the total flow rate of the entire fracture and the total seepage flow rate, assuming equal seepage flow rates.

[0010] In one feasible implementation, according to The equivalent hydraulic radius is obtained. Where π is the mathematical constant pi; b is the actual crack aperture of the pressurized crack. The length of the crack along the longitudinal direction of the tunnel.

[0011] In one feasible implementation, the equivalent circular drainage holes are set in the tunnel lining boundary, and the distance between the equivalent circular drainage holes and the tunnel lining boundary approaches zero, and the distribution positions of the circular drainage holes are obtained. Specifically, this includes: identifying the actual pressurized crack positions of the tunnel lining boundary based on a two-dimensional diagram of the tunnel lining boundary; performing position replacement processing on the equivalent circular drainage hole positions after equivalent transformation according to the actual pressurized crack positions; and controlling the distance between the equivalent circular drainage hole positions and the tunnel lining boundary to approach zero based on the conflict between the mathematical singularity and boundary conditions of the seepage model; and obtaining the distribution positions of the circular drainage holes based on the equivalent structural position distribution of each equivalent circular drainage hole position.

[0012] In one feasible implementation, based on the continuity of groundwater seepage, a two-dimensional stable seepage control equation for the tunnel lining boundary is established and the boundary conditions are determined. Specifically, this includes: calculating the total head of the seepage field outside the tunnel lining boundary based on a rectangular coordinate system constructed from the tunnel cross section, considering pore water pressure, water unit weight, and positional head; using the total head of the seepage field, performing two-dimensional seepage differential calculations based on homogeneous and isotropic aquifers to obtain a two-dimensional stable seepage control equation for analyzing the seepage field outside the tunnel lining boundary; and controlling the boundary conditions of groundwater outlet head, head under free drainage boundary of equivalent circular drainage holes, and impermeable boundary of the tunnel lining to generate the boundary conditions. The two-dimensional stable seepage control equation and the boundary conditions are prerequisites for seepage analysis of multiple connected domains outside the tunnel lining boundary.

[0013] In one feasible implementation, given the conditions of satisfying the equivalent hydraulic radius and the distribution location of the circular drainage holes, the horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under a conformal mapping to obtain a planar unit circle. Specifically, this includes: if the conditions of satisfying the equivalent hydraulic radius and the distribution location of the circular drainage holes are identified and met, the seepage region in the horseshoe-shaped physical plane under the tunnel cross-section is transformed into a regular unit circle region on the mapping plane; wherein, the lining edge in the horseshoe-shaped physical plane is mapped to the inner circle on the mapping plane, and the horizontal plane of the cross-section in the horseshoe-shaped physical plane is mapped to the outer circle on the mapping plane; wherein, the mapping relationship between the horseshoe-shaped physical plane and the mapping plane is a conformal mapping based on the Laurent series expansion; through the conformal mapping, the horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under a conformal mapping to obtain the planar unit circle after the equivalent transformation of the horseshoe-shaped non-circular boundary.

[0014] In one feasible implementation, before performing two-dimensional seepage alternating iterations on the excess hydraulic gradient generated by the equivalent circular drainage hole on the tunnel and the excess head generated by the tunnel on the equivalent circular drainage hole under multiple connected domains to obtain the hydraulic disturbance of the tunnel and the equivalent circular drainage hole after each alternating iteration correction, the method further includes: based on the two-dimensional stable seepage control equation and boundary conditions, splitting the multiple connected domain under the combination of the tunnel and the equivalent circular drainage hole into the single connected domain of the crack equivalent hole based on the equivalent circular drainage hole and the single connected domain of the tunnel as a whole; based on the boundary transformation rules corresponding to the planar unit circle, performing shape equivalence transformation processing on the single connected domain of the crack equivalent hole and the single connected domain of the tunnel related to the planar circle to obtain the single connected domain of the crack equivalent hole and the single connected domain of the tunnel after the planar circle transformation.

[0015] In one feasible implementation, based on the equivalent hole single-connected domain of the fracture and the tunnel single-connected domain, and based on the two-dimensional steady-state seepage control equation and boundary conditions, the redundant hydraulic gradient generated by the equivalent circular drainage hole on the tunnel and the redundant head generated by the tunnel on the equivalent circular drainage hole are subjected to two-dimensional seepage alternating iterations under the relevant multi-connected domains to obtain the hydraulic disturbance of the tunnel and the equivalent circular drainage hole after each alternating iteration correction. Specifically, this includes: in the first iteration, calculating the first redundant hydraulic gradient of the equivalent hole single-connected domain of the fracture on the tunnel single-connected domain, and applying it in reverse to the... The tunnel is used as a single connected domain to eliminate disturbances; the second excess head generated by the tunnel's single connected domain on the equivalent hole's single connected domain is calculated to obtain the first round of correction results; in subsequent iterations, the excess head obtained in the previous iteration is applied in reverse to the equivalent hole's single connected domain to calculate the new excess hydraulic gradient; and the new excess head generated by the tunnel's single connected domain on the equivalent hole's single connected domain is applied in reverse and calculated; until the iterated excess hydraulic gradients all meet the iteration convergence criterion, the hydraulic disturbance between the tunnel and the equivalent circular drainage hole after each alternating iteration correction is obtained.

[0016] In one feasible implementation, based on the corrected hydraulic disturbance and the initial hydraulic disturbance after each alternating iteration, the analytical results of the seepage field under the mutual influence of the tunnel and the equivalent circular drainage hole are calculated and obtained. Specifically, this includes: superimposing the corrected hydraulic disturbance obtained from all iterations with the initial hydraulic disturbance to obtain the multi-connected domain seepage characteristics of the tunnel lining in water-rich strata; and using the multi-connected domain seepage characteristics, performing data analysis on the water pressure distribution law of the tunnel lining and the infiltration characteristics of water outside the tunnel to obtain the analytical results of the seepage field under the mutual influence of the tunnel and the equivalent circular drainage hole.

[0017] On the other hand, this application also provides a seepage field analysis device for cracked lining in water-rich strata, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, so that the at least one processor can execute a seepage field analysis method for cracked lining in water-rich strata as described in any of the above embodiments.

[0018] This application provides a method and equipment for analyzing the seepage field of cracked linings in water-rich strata. Compared with the prior art, the embodiments of this application have the following beneficial technical effects: 1. Achieve quantitative equivalent transformation of complex cracks: Based on the strict flow equivalence derivation of the equivalent radius formula of parallel plate laminar flow (cubic law) and circular pipe laminar flow, the traditional geometric area equivalence and empirical simplification are abandoned, and a pure theoretical, approximation-free, and accurate equivalent of crack seepage is achieved, which truly reflects the actual seepage characteristics of lining cracks and greatly improves the accuracy of seepage field analysis.

[0019] 2. Accurate solution to seepage problems in multiple connected domains: The Schwartz alternating method is used to decompose multiple connected domains and iteratively correct hydraulic disturbances. For the first time, the mutual interference between tunnels and cracks is accurately considered. The calculation results are far superior to existing analysis methods that ignore disturbances, which greatly improves the accuracy of seepage field analysis.

[0020] 3. Solving the problem of seepage modeling for non-circular cross-section linings: By using conformal mapping, the complex boundary of the horseshoe-shaped non-circular cross-section is transformed into a regular unit circle boundary, filling the technical gap that existing technologies cannot accurately analyze the seepage field of "complex cracks + non-circular cross-section" linings, and adapting to the mainstream non-circular cross-section tunnel lining forms in engineering.

[0021] 4. The analytical model combines accuracy and efficiency: The established two-dimensional analytical model can be used as a theoretical support. Compared with the three-dimensional numerical simulation method, the solution process is simple and the amount of calculation is small. It can quickly obtain the distribution law of seepage field and external water pressure, which greatly improves the efficiency of engineering application. Moreover, the results are highly universal and can be adapted to different water-rich strata tunnel engineering scenarios.

[0022] 5. Meets the actual application needs of engineering: The technical solution of this application is based entirely on the parameters that can be obtained in actual engineering and the common tunnel forms in engineering. The analysis results can directly provide reliable theoretical data support for the analysis of the disaster mechanism of cracking lining of tunnels in water-rich strata and the design of protection and reinforcement. It has important practical engineering value for improving the safety and stability of tunnel projects in water-rich strata.

[0023] 6. The technical system is complete and expandable: The technical system of "permeability equivalence + Schwartz alternating method + conformal mapping method" constructed in this application can be expanded to seepage analysis of cracks of different shapes and linings of different non-circular cross sections according to actual engineering needs, and has good technical expandability. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 A flowchart illustrating a method for analyzing the seepage field in a cracked lining of a water-rich stratum, as provided in this application embodiment; Figure 2 A schematic diagram of an equivalent structure of a circular drainage hole based on the lining boundary is provided for an embodiment of this application; Figure 3 A schematic diagram illustrating the alternating iteration of hydraulics and head based on seepage in multiple connected domains, provided in an embodiment of this application; Figure 4 A schematic diagram of the boundary transformation of a horseshoe-shaped non-circular cross section based on conformal mapping is provided for an embodiment of this application; Figure 5 This is a schematic diagram of the structure of a seepage field analysis device for cracked lining in water-rich strata provided in this application embodiment. Detailed Implementation

[0025] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0026] It should be noted that the core problems and shortcomings of traditional existing technologies for analyzing the seepage field of cracked linings in water-rich strata are as follows: 1) Complex cracks cannot be directly analyzed and modeled: The morphology, size and permeability characteristics of lining cracks are complex and diverse. They are irregular and unquantifiable permeability boundaries. Existing technologies do not have an effective method to transform them into regular seepage boundaries, and they cannot be directly incorporated into the seepage field control equations for solution. This is the core technical obstacle to seepage analysis of cracked linings.

[0027] 2) Poor practicality of three-dimensional numerical simulation methods: This method relies solely on numerical calculations and lacks theoretical analytical model support. The solution process is complex and computationally intensive, and the results lack universality, making it difficult to quickly adapt to different engineering scenarios. As a result, the efficiency and cost of engineering applications are low.

[0028] 3) The mutual interference between tunnels and cracks is not considered: Existing methods do not take into account the hydraulic disturbance between tunnels and cracks in the seepage solution, which makes it impossible to obtain an accurate solution for the seepage problem in multiple connected domains, and the calculation results cannot reflect the actual seepage field distribution law.

[0029] In other words, the core difficulty in solving the above problems lies in finding a quantitative and controllable method to transform the seepage behavior of complex cracks into regular and quantifiable seepage boundaries, while solving the technical challenges of non-circular cross-section boundary transformation and multi-connected domain seepage solution. The goal is to achieve an organic combination of these three aspects to establish an analytical model that is suitable for engineering practice. This is the seepage field analysis method for cracked linings in water-rich strata provided in the embodiments of this application.

[0030] This application provides a method for analyzing the seepage field of cracked linings in water-rich formations. Through a step-by-step technical solution of "fracture permeability equivalent transformation → multi-connected domain seepage solution → non-circular section boundary transformation," it achieves accurate analysis of the seepage field in cracked linings of water-rich formations. The overall technical solution revolves around the core of permeability equivalence, combining the Schwartz alternation method and conformal mapping method to construct a complete seepage analysis system, such as... Figure 1 As shown, the method for analyzing the seepage field of cracked linings in water-rich strata specifically includes steps S101-S106: S101. Based on the total flow rate of the entire pressurized fracture, perform equivalent permeability calculations on the equivalent circular drainage holes under the relevant total seepage flow rate to obtain the equivalent hydraulic radius of the equivalent circular drainage holes after the fracture is equivalently transformed. That is, based on the principle of permeability equivalence, the direct simulation of the fracture geometry is abandoned, and the equivalent matching of the overall permeability behavior is pursued. The complex permeability behavior of the lining fracture is equivalent to the regular drainage behavior of the circular drainage holes near the lining, realizing the regularization and quantifiable transformation of the complex permeability boundary.

[0031] Specifically, based on the principle of permeability equivalence, the actual pressurized fracture is subjected to equivalent processing of key permeability parameters such as permeability flow rate per unit length, permeability velocity, and drainage pressure to obtain an equivalent circular drainage hole. The equivalent circular drainage hole is equivalent to the overall permeability behavior of the actual pressurized fracture.

[0032] As a feasible implementation method, based on the principle of permeability equivalence, it is necessary to ensure that the equivalent circular drainage hole is completely consistent with the actual lining crack in terms of three key permeability parameters: permeation flow rate per unit length, permeation velocity, and drainage pressure. This ensures that the equivalent seepage field results can truly reflect the permeability effect of cracks in actual engineering. In other words, it is necessary to abandon the direct simulation of crack geometry and pursue the equivalent matching of overall permeability behavior, equating the complex permeability behavior of lining cracks with the regular drainage behavior of nearby circular drainage holes around the lining, thereby achieving the regularization and quantification of complex permeability boundaries.

[0033] Furthermore, it is necessary to obtain the actual seepage flow per unit length of the pressurized crack based on the gravitational acceleration, the crack opening of the tunnel lining, the water motion viscosity coefficient, the head difference between the two ends of the crack, and the lining thickness; and to obtain the total flow of the entire crack based on the longitudinal length of the crack along the tunnel.

[0034] In one embodiment, it is necessary to first determine the formula for calculating the actual seepage flow rate of the pressurized fracture: the seepage flow of the pressurized fracture conforms to the parallel plate laminar flow theory (cubic law), and belongs to the Poiseuille flow of viscous fluid in a narrow slit. Combining the seepage characteristics of the fracture, the actual seepage flow rate per unit length of the pressurized fracture is... The calculation formula is: ;in, It is the acceleration due to gravity. For crack opening, Let be the kinematic viscosity coefficient of water. Due to the difference in water head at both ends of the crack, The thickness of the lining is given. Next, the total flow rate along the entire crack is calculated. for: .

[0035] Furthermore, based on the fact that the seepage in the equivalent circular drainage hole is laminar flow in a circular pipe, and using the Hagen–Poiseuille law, the total seepage flow of the equivalent circular drainage hole is determined.

[0036] In one embodiment, it is also necessary to determine the formula for calculating the seepage flow of the equivalent circular drainage hole: the seepage of the equivalent circular drainage hole is laminar flow in a circular pipe, which conforms to the Hagen–Poiseuille law, and its total seepage flow... The calculation formula is: ;in, The radius of the equivalent circular drainage hole is... This represents pi (π), and the meanings of the other parameters are the same as described above.

[0037] Furthermore, the total flow rate of the entire crack and the total seepage flow rate are combined under the condition that the seepage flow rates are equal to obtain the equivalent hydraulic radius of the equivalent circular drainage hole after the crack is equivalently transformed.

[0038] As a possible implementation method, according to The equivalent hydraulic radius is obtained. Where π is the mathematical constant pi; b is the actual crack aperture of the pressurized crack; This represents the longitudinal length of the crack along the tunnel. This equivalent formula can be used to represent the lining crack (aperture). Longitudinal length Precisely equivalent to a circular drainage hole (radius) This makes the flow rate, head, and hydraulic effects of the two completely equivalent.

[0039] In one embodiment, a theoretical formula is derived based on the principle of permeability equivalence: that is, according to the core requirement of permeability equivalence, the total seepage flow of the actual crack is equal to that of the equivalent circular drainage hole. = Solve the two seepage flow formulas simultaneously: Then eliminate the identical parameters on both sides of the equation. , , , After further refinement, a rigorous theoretical formula for calculating the radius of the equivalent circular drainage hole is obtained: .

[0040] As a feasible implementation method, in a specific implementation, for pressurized drainage cracks commonly seen in engineering, the hydraulic radius r of the equivalent circular drainage hole can be calculated using the quantitative calculation formula r=V / Q, based on the unit length crack flow rate Q and seepage velocity V that can be directly obtained from on-site engineering monitoring and indoor tests. Finally, this method can be used to verify the theoretical calculation formula to ensure that the theoretical calculation formula guarantees that the permeability of the circular drainage hole is highly consistent with the actual crack, thus laying the foundation for subsequent analytical modeling.

[0041] S102. The equivalent circular drainage holes are set in the tunnel lining boundary, and the distance between the equivalent circular drainage holes and the tunnel lining boundary approaches zero, and the distribution position of the circular drainage holes is obtained.

[0042] Specifically, the first step is to identify the actual location of pressurized cracks at the tunnel lining boundary based on a two-dimensional diagram of the tunnel lining boundary.

[0043] Furthermore, based on the actual location of the pressurized cracks, the locations of the equivalent circular drainage holes after equivalent transformation are replaced. And based on the conflict between the mathematical singularity and boundary conditions of the seepage model, the distance between the locations of the equivalent circular drainage holes and the tunnel lining boundary is controlled to approach zero. Finally, based on the equivalent structural location distribution of each equivalent circular drainage hole location, the distribution location of the circular drainage holes is obtained.

[0044] In one embodiment, Figure 2 A schematic diagram of an equivalent structure of a circular drainage hole based on the lining boundary is provided for an embodiment of this application, as shown below. Figure 2 As shown in Figure 3, the equivalent circular drainage hole is placed close to the perimeter of the lining, so that the distance d between it and the lining boundary approaches 0, rather than being strictly equal to 0. The reason is that if the distance is directly taken as 0, the permeable boundary of the equivalent drainage hole will completely coincide with the impermeable boundary of the lining, causing a conflict between the mathematical singularity of the seepage model and the boundary conditions, resulting in no solution for the analytical equation or non-convergence of the calculation; by using the infinite approximation setting of d→0, it can accurately simulate the real characteristics of the crack being tightly attached to the lining wall and directly seeping in, and can also ensure that the mathematical model of the seepage field is solvable, stable and convergent, so that the equivalent structure is highly consistent with the seepage behavior of cracks in actual engineering.

[0045] S103. Based on the continuity of groundwater seepage, establish the two-dimensional steady-state seepage control equations for the tunnel lining boundary and determine the boundary conditions.

[0046] It should be noted that after completing the equivalent transformation of cracks, the seepage field analysis object is determined as a combination system of "tunnel + regular circular drainage hole". To simplify the calculation and ensure that the model is compatible with the actual engineering, five basic assumptions need to be set first, and then a two-dimensional steady-state seepage control equation is established. The basic assumptions include: ① The soil around the tunnel is a permeable isotropic medium, and the permeability coefficient of the surrounding rock is constant; ② The equivalent circular drainage hole can drain water freely, and the seepage is in a steady state; ③ The water flow obeys Darcy's law; ④ The tunnel and the equivalent circular drainage hole are infinitely long, and the plane strain condition is satisfied in the longitudinal direction (the seepage physical quantities are independent of the longitudinal coordinate, and there is no longitudinal seepage); ⑤ The thickness of the tunnel lining is not considered, and the lining is an impermeable boundary.

[0047] Specifically, based on the rectangular coordinate system constructed by the tunnel cross section, the total head of the seepage field outside the tunnel lining boundary is calculated for the pore water pressure, water unit weight, and positional head.

[0048] Furthermore, by using the total head of the seepage field, a two-dimensional seepage differential calculation based on a homogeneous and permeable isotropic aquifer is performed on the seepage field outside the tunnel lining boundary, resulting in a two-dimensional stable seepage control equation for the analysis of the seepage field outside the tunnel lining boundary.

[0049] In one embodiment, based on the principle of continuity of groundwater seepage, the fundamental differential governing equations for two-dimensional steady-state seepage of a homogeneous, isotropic aquifer in a rectangular coordinate system are established as follows: The total head of the seepage field is calculated as h=u / γ+y (u is the pore water pressure, γ is the specific weight of water, and y is the position head).

[0050] Furthermore, it is necessary to control the boundary conditions in the seepage field, including the groundwater head at the groundwater level, the head at the equivalent circular drainage hole boundary (which is a free drainage boundary), and the tunnel lining boundary (which is an impermeable boundary), to generate boundary conditions. That is, three types of boundary conditions need to be set based on the basic assumptions: ① the head at the groundwater level is 0; ② the head at the equivalent circular drainage hole boundary is a free drainage boundary; ③ the tunnel lining boundary is an impermeable boundary, satisfying the radial seepage condition. The pre-constructed two-dimensional stable seepage control equations and boundary conditions are prerequisites for seepage analysis in multiple connected domains outside the tunnel lining boundary; that is, they serve as the basic conditions or data basis for subsequent processing of seepage problems in multiple connected domains.

[0051] S104. Under the condition of satisfying the equivalent hydraulic radius and the distribution position of the circular drainage holes, the horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under the relevant conformal mapping to obtain a planar unit circle.

[0052] Specifically, if the equivalent hydraulic radius and the distribution location of the circular drainage holes are identified and satisfied, the seepage region in the horseshoe-shaped physical plane under the tunnel cross-section is transformed into a regular unit circle region on the mapping plane. Specifically, the lining edge in the horseshoe-shaped physical plane is mapped to the inner circle on the mapping plane, and the horizontal plane of the cross-section in the horseshoe-shaped physical plane is mapped to the outer circle on the mapping plane. The mapping relationship between the horseshoe-shaped physical plane and the mapping plane is a conformal mapping based on the Laurent series expansion.

[0053] Furthermore, by using conformal mapping, the horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under the relevant conformal mapping, resulting in a planar unit circle after the horseshoe-shaped non-circular boundary has been equivalently transformed.

[0054] In one embodiment, Figure 4 A schematic diagram of the boundary transformation of a horseshoe-shaped non-circular cross-section based on conformal mapping is provided for an embodiment of this application, as shown below. Figure 4 As shown: In the physical plane z, x and y are a pair of coordinate axes; in the mapping plane ξ, τ and σ are also a pair of coordinate axes, where the radius of the outer ring is unit 1 and the radius of the inner ring is ρ. To address the problem of the complex boundary of the horseshoe-shaped non-circular cross-section lining being unsolvable directly, in each iteration step of the subsequent Schwartz alternation method, a conformal mapping method is used to transform the complex boundary into a regular unit circle boundary. The specific implementation is as follows: 1) Mapping target: Transform the seepage region with horseshoe-shaped complex boundary on the physical plane z into a regular unit circle region on the mapping plane ξ, where the outer edge of the lining is mapped to an inner circle with radius ρ on the ξ plane, and the horizontal plane is mapped to an outer circle with radius 1 on the ξ plane.

[0055] 2) Mapping Formula: The conformal mapping formula is expressed using the Laurent series expansion, specifically as follows: ;in, For physical plane complex variables, Let i be a complex variable representing the mapping plane (where i is the imaginary unit and θ is the polar angle), and R be a positive real number related to the tunnel cross-sectional dimensions. Here, k represents the polynomial coefficients, k is a natural number starting from 0, and n is the number of polynomial terms (the more complex the cross-section, the larger the value of n, and the better the mapping effect).

[0056] 3) Solution of non-circular cross section: The seepage problem of non-circular cross section is transformed into a simple seepage problem of unit circle by conformal mapping. The seepage field of single hole is solved in each iteration step. Finally, the results of the subsequent Schwartz alternation method are combined to obtain the analytical results of the seepage field of non-circular cross section lining.

[0057] S105. Based on the single connected domain of the equivalent hole of the crack and the single connected domain of the tunnel under the unit circle of the plane, and based on the two-dimensional steady seepage control equation and boundary conditions, the excess hydraulic gradient generated by the equivalent circular drainage hole on the tunnel and the excess water head generated by the tunnel on the equivalent circular drainage hole are subjected to two-dimensional seepage alternating iteration under the relevant multi-connected domains to obtain the hydraulic disturbance of the tunnel and the equivalent circular drainage hole after each alternating iteration correction.

[0058] Specifically, based on the two-dimensional steady-state seepage control equation and boundary conditions, the multi-connected domain under the combination of tunnel and equivalent circular drainage hole needs to be decomposed into a single-connected domain of crack equivalent hole based on equivalent circular drainage hole and a single-connected domain of the entire tunnel.

[0059] In one embodiment, Figure 3 A schematic diagram illustrating the alternating iteration of hydraulics and head based on seepage in multiple connected domains, as provided in this application embodiment, is shown below. Figure 3 As shown, after determining the two-dimensional steady-state seepage control equations and boundary conditions, the combined system of "tunnel + equivalent circular drainage hole" belongs to the steady-state seepage problem of a semi-infinite multi-connected domain. The two systems have mutual hydraulic interference and cannot be solved directly. Therefore, the Schwartz alternating method is used to achieve an analytical solution. Its core is to split the complex multi-connected domain into two simply connected domains and alternately iterate to correct the disturbance. That is, the multi-connected domain is split into two independent simply connected domains: the tunnel simply connected domain and the crack equivalent hole simply connected domain, and the seepage characteristics of the two are analyzed separately.

[0060] Furthermore, based on the boundary transformation rules corresponding to the planar unit circle, the crack equivalent hole simple connected domain and the tunnel simple connected domain are subjected to shape equivalence transformation processing related to the planar circle, resulting in the crack equivalent hole simple connected domain and the tunnel simple connected domain after planar circle transformation.

[0061] Furthermore, in the first iteration, the first redundant hydraulic gradient of the fracture equivalent hole simply connected domain to the tunnel simply connected domain is calculated and applied in reverse to the tunnel simply connected domain to eliminate disturbance. Then, the second redundant hydraulic head generated by the tunnel simply connected domain to the fracture equivalent hole simply connected domain is calculated, yielding the first round of correction results.

[0062] Furthermore, in the iteration, the excess hydraulic head obtained in the previous iteration is applied in reverse to the simply connected domain of the equivalent hole of the fracture, and a new excess hydraulic gradient is calculated. The new excess hydraulic head generated by the simply connected domain of the tunnel on the simply connected domain of the equivalent hole of the fracture is also applied in reverse and calculated. Finally, until the excess hydraulic gradient (excess hydraulic head) obtained in each iteration satisfies the iteration convergence criterion, the hydraulic disturbance between the tunnel and the equivalent circular drainage hole after each alternating iteration correction is obtained.

[0063] In one embodiment, such as Figure 3As shown, firstly, the boundary transformation rule corresponding to the unit circle in the plane is used to perform shape equivalence transformation processing on the equivalent hole simple connected domain of the crack and the simple connected domain of the tunnel, which are obtained after the transformation of the plane circle into the equivalent hole simple connected domain of the crack and the simple connected domain of the tunnel. Then, the Schwartz alternating method is used to solve the seepage problem of multiple connected domains. In the alternating iteration process, it includes: 1) First iteration: Calculate the redundant hydraulic gradient (redundant head) p12 generated by the equivalent hole simple connected domain of the crack on the simple connected domain of the tunnel, and apply it in reverse to the simple connected domain of the tunnel to eliminate the disturbance; then calculate the redundant hydraulic gradient (redundant head) p11 generated by the simple connected domain of the tunnel on the equivalent hole simple connected domain of the crack, complete the first round of correction, and obtain the first round of correction results. It should be noted that in Figure 3 In the example: -p12 is the force in the opposite direction of the redundant hydraulic gradient p12, which is the reverse redundant hydraulic gradient; -p22 is the force in the opposite direction of the redundant hydraulic gradient p22, which is also the reverse redundant hydraulic gradient.

[0064] 2) After obtaining the first round of correction results, the second iteration is carried out: First, the excess hydraulic gradient p11 in the first round of correction results is applied in reverse to the excess hydraulic gradient p22 caused by the equivalent tunnel periphery of the crack around the tunnel periphery; then, the excess hydraulic gradient p22 is applied in reverse to the excess hydraulic gradient p21 caused by the equivalent tunnel periphery of the crack around the tunnel periphery.

[0065] 3) Then in subsequent iterations: apply the redundant hydraulic gradient obtained in the previous round in reverse to the single connected domain of the equivalent hole of the fracture (the periphery of the equivalent tunnel of the fracture), calculate the new redundant hydraulic gradient generated by the single connected domain of the equivalent hole of the fracture on the single connected domain of the tunnel, and then apply and calculate the new redundant hydraulic gradient (new redundant head) generated by the single connected domain of the tunnel on the single connected domain of the equivalent hole of the fracture, and iterate repeatedly.

[0066] 4) During iterative convergence: The "redundant hydraulic gradient / head" generated in each iteration continuously decreases. When the value drops to the preset accuracy requirement, that is, after the redundant hydraulic gradients generated by the iteration all meet the iterative convergence criterion, the iteration stops, thus obtaining the hydraulic disturbance between the tunnel and the equivalent circular drainage hole after each alternating iteration correction. That is: the Schwartz alternating method is used to decompose the multi-connected domain, the hydraulic disturbance between the tunnel and the equivalent drainage hole is iteratively corrected alternately, and finally the horseshoe-shaped non-circular cross section is transformed into a ξ-plane unit circle through conformal mapping, completing the solution of the seepage of the single hole (crack equivalent hole / tunnel hole) in each iteration step.

[0067] S106. Based on the corrected hydraulic disturbance and initial hydraulic force after each alternating iteration, the analytical results of the seepage field under the mutual influence of the tunnel and the equivalent circular drainage hole are calculated and obtained.

[0068] Specifically, the corrected hydraulic disturbances obtained from all iterative corrections are first superimposed with the initial hydraulic disturbances to obtain the multi-connected domain seepage characteristics of the tunnel lining in water-rich strata. Then, based on the multi-connected domain seepage characteristics, the water pressure distribution law of the tunnel lining and the infiltration characteristics of water outside the tunnel are analyzed to obtain the analytical results of the seepage field under the mutual influence of the tunnel and the equivalent circular drainage hole.

[0069] As a feasible implementation method, the corrected solution (corrected hydraulic disturbance) of all iteration steps is superimposed with the initial solution (initial hydraulic disturbance), and the distribution law of external water pressure in the lining and the infiltration characteristics of external water are analyzed. The accurate seepage field analysis results of the seepage field under the mutual influence of the tunnel and the equivalent pore of the crack are obtained, which can help the seepage analysis in the construction and operation stages of tunnel engineering in water-rich strata.

[0070] In one embodiment, the core technical solution of this application can be partially replaced and extended. All the partially replaced solutions can achieve the analytical solution of the seepage field of the cracked lining in water-rich strata, and do not depart from the core protection scope of this invention. The available alternative solutions are as follows: 1. Equivalent drainage hole cross-section replacement: Cracks can be equivalent to circular drainage holes, and in practical applications, they can be replaced by drainage holes with regular cross-sections such as elliptical, square, and rectangular. It is only necessary to re-derive the equivalent hydraulic parameter calculation formula based on the flow equivalence relationship between laminar flow on parallel flat plates and laminar flow on corresponding cross-sections, and keep the seepage flow, seepage velocity, and drainage pressure per unit length consistent to achieve equivalent transformation.

[0071] 2. Equivalent radius calculation method alternative: In engineering, the field monitoring / indoor test fitting formula: r=V / Q can be used as an alternative; the two can be mutually verified and selected as needed, and both can achieve the equivalent permeability of cracks and drainage holes.

[0072] 3. Replacement of conformal mapping formula and method: The Loren series expansion used in this application to realize the non-circular section mapping can be replaced by conformal mapping methods such as fractional linear mapping, polynomial mapping, and elliptic function mapping, which are suitable for horseshoe-shaped, circular, and rectangular tunnel sections; it is only necessary to accurately transform the complex boundary of the physical plane into a regular circular boundary to meet the solution requirements.

[0073] 4. Alternative methods for solving multi-connected domains: The Schwartz alternation method used in this application to solve seepage in multi-connected domains can be replaced by analytical methods such as complex function method, Green's function method, and superposition principle method; by splitting the solution domain and correcting the hydraulic disturbance terms, the analytical seepage field under the interaction between the tunnel and the equivalent drainage hole can be realized.

[0074] 5. Iterative convergence control standard replacement: This application uses the reduction of excess head / excess hydraulic gradient to a threshold as the convergence standard, which can be replaced by fixed number of iterations, relative error control, etc.; the convergence conditions can be adjusted according to different engineering accuracy requirements, and the analytical results can be guaranteed to meet the engineering application requirements.

[0075] 6. Alternative methods for obtaining seepage parameters: Crack geometric parameters and seepage parameters can be obtained through on-site monitoring and laboratory tests. When there are no actual measurement conditions, alternative methods such as looking up tables in standards, numerical simulation inversion, and engineering analogy can be used. The source of parameters does not affect the core process of equivalent transformation and analytical solution.

[0076] In addition, this application also provides a device for analyzing the seepage field of cracked linings in water-rich strata, such as... Figure 5 As shown, the 500-unit seepage field analysis equipment for cracked linings in water-rich strata specifically includes: At least one processor 501; and a memory 502 communicatively connected to the at least one processor 501; wherein the memory 502 stores instructions executable by the at least one processor 501 to enable the at least one processor 501 to execute: Based on the total flow rate of the entire actual pressurized fracture, the equivalent circular drainage hole is subjected to a seepage equivalent calculation under the relevant total seepage flow rate to obtain the equivalent hydraulic radius of the equivalent circular drainage hole after the fracture is equivalently transformed. Equivalent circular drainage holes are set in the tunnel lining boundary, and the distance between the equivalent circular drainage holes and the tunnel lining boundary approaches zero, thus obtaining the distribution position of the circular drainage holes. Based on the continuity of groundwater seepage, a two-dimensional steady-state seepage control equation for the tunnel lining boundary is established and the boundary conditions are determined. Under the conditions of satisfying the equivalent hydraulic radius and the distribution position of the circular drainage holes, the horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under the relevant conformal mapping to obtain a planar unit circle. Based on the single connected domain of the equivalent hole of the crack and the single connected domain of the tunnel under the unit circle of the plane, and based on the two-dimensional steady seepage control equation and boundary conditions, the excess hydraulic gradient generated by the equivalent circular drainage hole to the tunnel and the excess water head generated by the tunnel to the equivalent circular drainage hole are subjected to two-dimensional seepage alternating iteration under the relevant multi-connected domains to obtain the hydraulic disturbance of the tunnel and the equivalent circular drainage hole after each alternating iteration correction. Based on the corrected hydraulic disturbance and the initial hydraulic force after each alternating iteration, the analytical results of the seepage field under the mutual influence of the tunnel and the equivalent circular drainage hole are calculated and obtained.

[0077] This application addresses the core problem of complex cracks' inability to be analytically modeled by equating the complex seepage behavior of lining cracks to the regular drainage behavior of near-circular drainage holes around the lining and providing a quantitative calculation formula for the equivalent hydraulic radius. Based on this, the Schwartz alternation method is used to solve the seepage problem in multiple connected domains formed by the tunnel and the equivalent drainage holes, accurately considering their mutual interference. Simultaneously, the conformal mapping method is combined to transform the complex boundary of the horseshoe-shaped non-circular cross-section into a regular unit circle boundary. Finally, a two-dimensional analytical model of the seepage field of the non-circular cracked lining is established and solved, achieving accurate and efficient analysis of the seepage field and external water pressure distribution law of cracked linings in water-rich strata. This provides reliable theoretical data support for the analysis of the disaster mechanism and the design of protection and reinforcement of cracked linings in water-rich strata tunnels, filling a gap in existing technologies.

[0078] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the device embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0079] The foregoing has described specific embodiments of this application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired results. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0080] The above description is merely an embodiment of this application and is not intended to limit this application. For those skilled in the art, various modifications and variations can be made to the embodiments of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the embodiments of this application should be included within the specification of this application.

Claims

1. A method of analyzing a fracture-liner flow field in a water- rich formation, comprising: The method includes: Based on the total flow rate of the entire actual pressurized fracture, the equivalent circular drainage hole is subjected to a seepage equivalent calculation under the relevant total seepage flow rate to obtain the equivalent hydraulic radius of the equivalent circular drainage hole after the fracture is equivalently transformed. The equivalent circular drainage holes are set in the tunnel lining boundary, and the distance between the equivalent circular drainage holes and the tunnel lining boundary approaches zero, thus obtaining the distribution position of the circular drainage holes. Based on the continuity of groundwater seepage, a two-dimensional steady-state seepage control equation for the tunnel lining boundary is established and the boundary conditions are determined. Under the conditions of satisfying the equivalent hydraulic radius and the distribution position of the circular drainage holes, the horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under relevant conformal mapping to obtain a planar unit circle. Based on the single connected domain of the equivalent hole of the crack and the single connected domain of the tunnel under the unit circle of the plane, and based on the two-dimensional steady seepage control equation and boundary conditions, the excess hydraulic gradient generated by the equivalent circular drainage hole to the tunnel and the excess water head generated by the tunnel to the equivalent circular drainage hole are subjected to two-dimensional seepage alternating iteration under the relevant multi-connected domains to obtain the hydraulic disturbance of the tunnel and the equivalent circular drainage hole after each alternating iteration correction. Based on the corrected hydraulic disturbance and the initial hydraulic force after each alternating iteration, the analytical results of the seepage field under the mutual influence of the tunnel and the equivalent circular drainage hole are calculated and obtained.

2. The method of fracture liner flow field analysis for water- rich formations of claim 1, wherein, Based on the total flow rate of the entire pressurized fracture, a permeability equivalent calculation is performed on the equivalent circular drainage hole under the relevant total seepage flow rate to obtain the equivalent hydraulic radius of the equivalent circular drainage hole after the fracture is equivalently transformed. Specifically, this includes: Based on the principle of permeability equivalence, the actual pressurized fracture is subjected to equivalent processing of key permeability parameters such as permeability flow rate per unit length, permeability velocity, and drainage pressure to obtain the equivalent circular drainage hole; wherein, the equivalent circular drainage hole is equivalent to the overall permeability behavior of the actual pressurized fracture. Based on the gravitational acceleration, the crack opening of the tunnel lining, the water kinematic viscosity coefficient, the head difference between the two ends of the crack, and the lining thickness, the seepage flow per unit length of the actual pressurized crack is obtained; and based on the longitudinal length of the crack along the tunnel, the total flow of the entire crack is obtained. Based on the fact that the seepage in the equivalent circular drainage hole is laminar flow in a circular pipe, and based on the Hagen–Poiseuille law, the total seepage flow of the equivalent circular drainage hole is determined. The equivalent hydraulic radius of the equivalent circular drainage hole after the crack is obtained by combining the total flow rate of the entire crack and the total seepage flow rate under the condition that the seepage flow rate is equal.

3. The method for analyzing the seepage field of cracked lining in water-rich strata according to claim 2, characterized in that, According to , the equivalent hydraulic radius is obtained; wherein π is the circular constant; b is the fracture opening of the actual fracture with pressure; is the length of the fracture along the longitudinal length of the tunnel.

4. The method for analyzing the seepage field of cracked lining in water-rich strata according to claim 1, characterized in that, The equivalent circular drainage holes are positioned within the tunnel lining boundary, with the distance between the equivalent circular drainage holes and the tunnel lining boundary approaching zero. The distribution of the circular drainage holes is then determined, specifically including: Based on a two-dimensional diagram of the tunnel lining boundary, the actual location of pressurized cracks at the tunnel lining boundary is identified. Based on the actual location of the pressurized crack, the location of the equivalent circular drainage hole after equivalent transformation is replaced; and based on the conflict between the mathematical singularity and boundary conditions of the seepage model, the distance between the location of the equivalent circular drainage hole and the tunnel lining boundary is controlled to approach zero. The distribution of the circular drainage holes is obtained based on the equivalent structural position distribution of each equivalent circular drainage hole position.

5. The method for analyzing the seepage field of cracked lining in water-rich strata according to claim 1, characterized in that, Based on the continuity of groundwater seepage, a two-dimensional steady-state seepage control equation is established for the tunnel lining boundary, and the boundary conditions are determined, specifically including: Based on the rectangular coordinate system constructed by the tunnel section, the total head of the seepage field outside the tunnel lining boundary is calculated under the relevant pore water pressure, water unit weight, and positional head. Using the total head of the seepage field, a two-dimensional seepage differential calculation based on a homogeneous and isotropic aquifer is performed on the seepage field outside the tunnel lining boundary to obtain a two-dimensional steady-state seepage control equation for the analysis of the seepage field outside the tunnel lining boundary. The boundary conditions are generated by controlling the groundwater head at the seepage field, the head at the equivalent circular drainage hole boundary under the free drainage boundary, and the boundary of the tunnel lining under the impermeable boundary. The two-dimensional steady-state seepage control equation and the boundary conditions are prerequisites for seepage analysis of multiple connected domains outside the tunnel lining boundary.

6. The method for analyzing the seepage field of cracked lining in water-rich strata according to claim 1, characterized in that, Under the conditions of satisfying the equivalent hydraulic radius and the distribution position of the circular drainage holes, the horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under relevant conformal mapping to obtain a planar unit circle, specifically including: If the equivalent hydraulic radius and the distribution location of the circular drainage holes are identified and satisfied, the seepage area in the horseshoe-shaped physical plane under the tunnel section is transformed into a regular unit circle area on the mapping plane; wherein, the lining edge in the horseshoe-shaped physical plane is mapped to the inner circle on the mapping plane, and the horizontal plane of the cross section in the horseshoe-shaped physical plane is mapped to the outer circle on the mapping plane. The mapping relationship between the horseshoe-shaped physical plane and the mapping plane is a conformal mapping based on the Laurent series expansion. By performing conformal mapping, the horseshoe-shaped non-circular boundary of the tunnel is transformed into a regular unit circle boundary under the relevant conformal mapping, resulting in the planar unit circle after the horseshoe-shaped non-circular boundary has been equivalently transformed.

7. The method for analyzing the seepage field of cracked lining in water-rich strata according to claim 1, characterized in that, Before performing alternating two-dimensional seepage iterations on the excess hydraulic gradient generated by the equivalent circular drainage hole on the tunnel and the excess head generated by the tunnel on the equivalent circular drainage hole under relevant multi-connected domains to obtain the hydraulic disturbance of the tunnel and the equivalent circular drainage hole after each alternating iteration correction, the method further includes: Based on the two-dimensional steady-state seepage control equation and boundary conditions, the multi-connected domain under the combination of tunnel and equivalent circular drainage hole is decomposed into the single-connected domain of the crack equivalent hole based on the equivalent circular drainage hole and the single-connected domain of the tunnel as a whole. Based on the boundary transformation rules corresponding to the planar unit circle, the crack equivalent hole simple connected domain and the tunnel simple connected domain are subjected to shape equivalence transformation processing related to the planar circle to obtain the crack equivalent hole simple connected domain and the tunnel simple connected domain after planar circle transformation.

8. The method for analyzing the seepage field of cracked lining in water-rich strata according to claim 7, characterized in that, Based on the single connected domain of the equivalent hole in the crack and the single connected domain of the tunnel, and based on the two-dimensional steady-state seepage control equation and boundary conditions, the redundant hydraulic gradient generated by the equivalent circular drainage hole on the tunnel and the redundant water head generated by the tunnel on the equivalent circular drainage hole are subjected to two-dimensional seepage alternating iterations under relevant multi-connected domains to obtain the hydraulic disturbances of the tunnel and the equivalent circular drainage hole after each alternating iteration correction, specifically including: In the first iteration, the first redundant hydraulic gradient of the equivalent hole single connected domain of the fracture to the single connected domain of the tunnel is calculated and applied in reverse to the single connected domain of the tunnel to eliminate the disturbance; the second redundant head generated by the single connected domain of the tunnel to the equivalent hole single connected domain of the fracture is calculated to obtain the first round of correction results; In subsequent iterations, the excess hydraulic head obtained in the previous iteration is applied in reverse to the single connected domain of the equivalent hole of the fracture, and a new excess hydraulic gradient is calculated; and the new excess hydraulic head generated by the single connected domain of the tunnel on the single connected domain of the equivalent hole of the fracture is applied in reverse and calculated. The process continues until all excess hydraulic gradients obtained through iteration meet the iteration convergence criterion, thus obtaining the hydraulic disturbance between the tunnel and the equivalent circular drainage hole after each alternating iteration correction.

9. The method for analyzing the seepage field of cracked lining in water-rich strata according to claim 1, characterized in that, Based on the corrected hydraulic disturbance and initial hydraulic conditions after each iterative correction, the analytical results of the seepage field under the interaction between the tunnel and the equivalent circular drainage hole are calculated and obtained, specifically including: The modified hydraulic disturbances obtained from all iterative corrections are superimposed with the initial hydraulic disturbances to obtain the multi-connected domain seepage characteristics of the tunnel lining cracked under water-rich strata. By analyzing the seepage characteristics of the multi-connected domains, the water pressure distribution law of the tunnel lining and the infiltration characteristics of water outside the tunnel are analyzed to obtain the analytical results of the seepage field under the mutual influence of the tunnel and the equivalent circular drainage hole.

10. A device for analyzing the seepage field of cracked linings in water-rich strata, characterized in that, The device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, enabling the at least one processor to perform a method for analyzing the seepage field of a cracked lining in a water-rich formation according to any one of claims 1-9.

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