Calculation method and system for three-dimensional steady seepage field of shield tunnel excavation face under boulder conditions

Abstract

This invention belongs to the field of shield tunneling technology, specifically a method and system for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions. It includes: S1 establishing a three-dimensional geometric model of the seepage field around the tunnel excavation face as a cuboid, with the vertical direction as the z-axis, the direction perpendicular to the tunnel excavation as the x-axis, and the direction along the tunnel excavation as the y-axis; S2, combining the boundary conditions of each region of the seepage field, establishing two-dimensional hydraulic head expressions for the six face regions of the three-dimensional geometric model based on the cuboid three-dimensional geometric model; S3 using the continuity conditions between regions to construct linear partial differential equations and Fourier series expansion equations, solving for the three-dimensional hydraulic head expressions for the six regions; and S4 obtaining the analytical solution for the hydraulic head at any position in the three-dimensional seepage field in front of the excavation face based on the superposition of Fourier series. This invention can accurately calculate the water pressure borne by the excavation face, which also has significant engineering significance for ensuring the safe construction of shield tunnels.

Description

Technical Field

[0001] This invention belongs to the field of shield tunneling technology, specifically a method and system for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions. Background Technology

[0002] With increasingly strained construction space resources in large cities, in addition to maximizing the use of surface and spatial resources, effectively utilizing underground space resources has become increasingly important. Urban underground engineering projects, exemplified by rail transit, have reached unprecedented scales. Water-rich sandy soil strata possess high permeability, low shear strength, and easily rheological properties. When shield tunnels are excavated in such strata, the stability of the excavation face is easily affected by obstacles such as boulders.

[0003] Isolated boulders, as common geological features in water-rich sandy soil strata, alter the stress distribution at the excavation face, leading to localized soil pressure concentration and consequently significant changes in the seepage field. Therefore, the impact of isolated boulders on excavation face stability has become a focus of engineering attention. Thus, proposing an analytical method with clear physical concepts and a certain level of computational accuracy, considering the presence of isolated boulders, is of great significance for theoretical research and engineering design of shield tunnel excavation face stability in water-rich strata.

[0004] Currently, research on analytical solutions for tunnel seepage fields both domestically and internationally mainly utilizes mathematical methods such as numerical simulation substitution and one-dimensional equation fitting to obtain simplified functional forms of the shield excavation face location. Furthermore, there are few reports on a method that possesses both high accuracy and a clear physical concept.

[0005] Therefore, there is no existing technology for calculating the three-dimensional seepage field in front of the tunnel excavation face that takes into account factors such as isolated boulders and seepage paths perpendicular to the tunnel direction, which is a technical problem that urgently needs to be solved. Summary of the Invention

[0006] To address the technical problem that existing technologies lack a method for calculating the three-dimensional steady-state seepage field of a tunnel excavation face after considering factors such as isolated boulders in front of the excavation face and seepage paths perpendicular to the tunnel direction, this invention provides a method and system for calculating the three-dimensional steady-state seepage field of a shield tunnel excavation face under isolated boulder conditions.

[0007] This invention adopts the following technical solution: a method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions, comprising: S1: A three-dimensional geometric model of the seepage field around the tunnel excavation face is established with the vertical direction as the z-axis, the direction perpendicular to the tunnel excavation as the x-axis, and the direction along the tunnel excavation as the y-axis. S2: Combining the boundary conditions of each region of the seepage field, based on the three-dimensional geometric model of the cuboid, establish the two-dimensional head expressions for the six face regions of the three-dimensional geometric model; S3: Used to construct linear partial differential control equations and Fourier series expansion equations using the continuity conditions between regions, and solve them to obtain the three-dimensional head expressions for the six regions; S4: Based on the superposition of Fourier series, the analytical solution of the water head at any position in the three-dimensional seepage field in front of the excavation face is obtained.

[0008] In some embodiments, in step S1, the three-dimensional geometric model is set as follows: The seepage state in front of the excavation face is a steady-state hydraulic head field, and the strata are homogeneous and isotropic; The tunnel lining and tunnel excavation face are impermeable boundaries with fixed pressure head h. F ; The water head at the far-field boundary of the ground is equal to the initial elevation h0 of the groundwater level; The initial elevation h0 of the groundwater level has sufficient surface groundwater recharge.

[0009] In some embodiments, step S2 includes: S21: The two-dimensional head expression for the six regions of the three-dimensional geometric model of the cuboid is as follows: in f 1( x, y ), f 2( x, y ), f 3( y, z ), f 4( x, z ), f 5( x, y )and f 6( x, z ) represents the expression for the boundaries of the six regions. f 6r (x, z) represents the semicircular boundary of the sixth face. f 6R (x, z) represents the region of the sixth face excluding the semicircle; f 1( x, y ), f 3( y, z )and f 4( x, z ) are known conditions; f 1( x, y ), f 3( y, z )and f 4( x, z ) are the water head at the far-field boundary of the land surface, both defined by h0; D The diameter of the shield excavation face. L1 represents the boundary length perpendicular to the tunnel boring direction. L 2 represents the boundary length along the tunnel boring direction; S22: Solve f 2( x, y The expression for ) is given, and then substituted into the two-dimensional head expression; S23: Solve f 5( x, y The expression for ) is given, and then substituted into the two-dimensional head expression; S24: Solve f 6( x, z The expression is given, and then substituted into the two-dimensional head expression.

[0010] In some embodiments, in S22, for f 2( x, y The seepage boundary conditions are represented by a rectangular region, and the mathematical expression for each boundary condition is as follows: in f 21 ( x )and f 23 ( y The given boundary conditions are: initial groundwater level and seepage head far from the excavation face, both equal to... h 0; Boundary conditions are fitted using approximate functional equations derived from numerical simulation. f 22 ( x )and f 24 ( y ),in f 21 ( x ), f 22 ( x ), f 23 ( y )as well as f 24 ( y ) are the boundary expressions for the two-dimensional region surfaces.

[0011] In some embodiments, in S23, for f 5( x, y The seepage boundary conditions are represented by a rectangular region, and the mathematical expression for each boundary condition is as follows: The corresponding coefficients a5k , b 5k , c 5k as well as d 5k As shown below, and k It is the expansion factor; ; f 52 ( y )and f 54 ( z The value was determined through numerical simulation.

[0012] In some embodiments, in S24, f 6( x, z The seepage boundary conditions are represented by a rectangular region, and the mathematical expression for each boundary condition is as follows: f 62 ( x )and f 64 ( z It was obtained through numerical simulation.

[0013] In some embodiments, step S3 includes: S31: Construct the partial differential governing equations: , , , ; S32: The analytical solution of the partial differential governing equation is expressed as: ; in , , , , , These are the boundary expressions for the six faces of the three-dimensional region.

[0014] S33: Yes , , , , , Solving for each, we get: in, .

[0015] In some embodiments, the numerical simulation process includes: Establish a three-dimensional finite difference numerical model; Based on the steady-state seepage assumption, the Laplace equation is solved using finite difference software, the head data of unknown boundary conditions are recorded, and parametric analysis is performed for different water level ratios. Using numerical simulation results, an approximate distribution equation for unknown boundary conditions is fitted, which is in the form of an exponential function.

[0016] A three-dimensional steady-state seepage field calculation system for the excavation face of a shield tunnel in water-rich sandy soil under isolated rock conditions, and a method for implementing this system, including: a model building module for establishing a three-dimensional geometric model by taking half a cross section based on symmetry, and defining a coordinate system with x, y, and z axes; The first calculation module is used to obtain the two-dimensional head expressions for the six regions based on Darcy's law and boundary conditions; The second calculation module is used to calculate the analytical solution of the head in the three-dimensional seepage field, and to calculate the analytical solution of the head at any position in the three-dimensional seepage field in front of the excavation face.

[0017] Compared with the prior art, the present invention has the following beneficial effects: This invention provides a method and system for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated boulder conditions. Based on symmetry, a half-section of the shield tunnel excavation face under isolated boulder conditions is used for calculation and analysis. The vertical direction is taken as the z-axis, the direction perpendicular to the tunnel excavation as the x-axis, and the direction along the tunnel excavation as the y-axis, establishing a three-dimensional geometric model of the seepage field around the tunnel excavation face. The seepage in the sand layer is isotropic and conforms to Darcy's law. Combining the boundary conditions of each region of the seepage field, the two-dimensional head expressions for the six regions of the three-dimensional geometric model are obtained using the method of separation of variables and the eigenfunction expansion method. Linear partial differential equations and Fourier series expansion equations are constructed using the continuity conditions between regions. After solving these equations, the three-dimensional head expressions for each region are obtained. Finally, based on the superposition of Fourier series, the analytical solution for the head at any position in the three-dimensional seepage field in front of the excavation face is obtained.

[0018] The present invention provides a method and system for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated boulder conditions. By quickly and accurately solving the water head at any point in the three-dimensional seepage field, it can quickly and conveniently analyze the influence of seepage conditions such as the location and shape of the isolated boulder on the water head distribution in the foundation pit, providing an accurate basis for the construction and protection of shield tunneling projects. It can also calculate the water pressure borne by the excavation face with relatively accurate results, which is of significant engineering importance for ensuring the safe construction of shield tunnels. Attached Figure Description

[0019] Figure 1 The water head boundary in front of the tunnel excavation face; Figure 2 The head boundary is f2(x, y); Figure 3 Let f5(y, z) be the head boundary; Figure 4 The head boundary is f6(x, z); Figure 5 f 22 (x) Comparison of the head distribution results obtained from the approximate distribution equation and the results obtained from numerical simulation; Figure 6 f 24 (y) Comparison of the head distribution results obtained from the approximate distribution equation and the results obtained from numerical simulation; Figure 7 The approximate distribution equation for the unknown boundary; Figure 8 To verify the effectiveness of the boundary condition fitting equation. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] A method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions includes: S1: A three-dimensional geometric model of the seepage field around the tunnel excavation face is established with the vertical direction as the z-axis, the direction perpendicular to the tunnel excavation as the x-axis, and the direction along the tunnel excavation as the y-axis. S2: Combining the boundary conditions of each region of the seepage field, based on the three-dimensional geometric model of the cuboid, establish the two-dimensional head expressions for the six face regions of the three-dimensional geometric model; S3: Used to construct linear partial differential control equations and Fourier series expansion equations using the continuity conditions between regions, and solve them to obtain the three-dimensional head expressions for the six regions; S4: Based on the superposition of Fourier series, the analytical solution of the water head at any position in the three-dimensional seepage field in front of the excavation face is obtained.

[0022] In a specific embodiment, step S1 requires some assumptions and simplifications to solve the seepage problem when solving the Laplace equation. First, it is assumed that the seepage state before the excavation face is a steady-state hydraulic head field, and the strata are homogeneous and isotropic. Second, an impermeable boundary and a fixed pressure head h are assumed for both the tunnel lining and the tunnel excavation face. F Assume the water head at the far-field boundary of the ground surface is equal to the initial elevation h0 of the groundwater level. Furthermore, assume that the initial elevation h0 of the groundwater level has sufficient surface groundwater recharge. The effective range of the water head distribution in front of the excavation face can be represented by a cuboid (e.g., ...). Figure 1 (As shown).

[0023] In some embodiments, step S2 includes: S21: The two-dimensional head expression for the six regions of the three-dimensional geometric model of the cuboid is as follows: in f 1( x, y ), f 2( x, y ), f 3( y, z ), f 4( x, z ), f 5( x, y )and f 6( x, z ) represents the expression for the boundaries of the six regions. f 6r (x, z) represents the semicircular boundary of the sixth face. f 6R (x, z) represents the region of the sixth face excluding the semicircle; f 1( x, y ), f 3( y, z )and f 4( x, z ) are known conditions; f 1( x, y ), f 3( y, z )and f 4( x, z ) are the water head at the far-field boundary of the land surface, both defined by h0; D The diameter of the shield excavation face.L 1 represents the boundary length perpendicular to the tunnel boring direction. L 2 represents the boundary length along the tunnel boring direction; S22: Solve f 2( x, y Find the expression for ) and substitute it into the two-dimensional head expression; S23: Solve f 5( x, y Find the expression for ) and substitute it into the two-dimensional head expression; S24: Solve f 6( x, z The expression is given, and then substituted into the two-dimensional head expression.

[0024] Specifically, in step S22, for f 2( x, y The seepage boundary condition is represented by a rectangular region (e.g., Figure 2 As shown), the mathematical expression for each boundary condition is: in f 21 ( x )and f 23 ( y The given boundary conditions are: initial groundwater level and seepage head far from the excavation face, both equal to... h 0; Boundary conditions are fitted using approximate functional equations derived from numerical simulation. f 22 ( x )and f 24 ( y ).in f 21 ( x ), f 22 ( x ), f 23 ( y )as well as f 24 ( y The following sections will describe the boundary expressions for two-dimensional regions, denoted as , respectively. f 5 and f 6. The same applies.

[0025] Specifically, in step S23, for f 5( x, y The seepage boundary conditions are represented by a rectangular region, and the mathematical expression for each boundary condition is as follows: The corresponding coefficients a 5k , b 5k , c 5k as well as d 5k As shown below, and k It is the expansion factor; f 52 ( y )and f 54 ( z The value was determined through numerical simulation.

[0026] Specifically, in step S24, for the sixth region of the seepage field f 6( x, z ), f 6( x, z The seepage boundary conditions are represented by a rectangular region, and the mathematical expression for each boundary condition is as follows: f 62 ( x )and f 64 ( z (Obtained through numerical simulation) f 62 ( x )and f 64 ( z The approximate function equation of ).

[0027] Specifically, step S3 includes: S31: Construct the partial differential governing equations: , , , ; S32: The analytical solution of the partial differential governing equation is expressed as: ; in , , , , , These are the boundary expressions for the six faces of the three-dimensional region; S33: Yes , , , , , Solving for each, we get: in, .

[0028] The numerical simulation process includes: 1) Establish a three-dimensional finite difference numerical model; 2) Based on the steady-state seepage assumption, the Laplace equation is solved using finite difference software, the head data of unknown boundary conditions are recorded, and parametric analysis is performed for different water level ratios; 3) Using the numerical simulation results, fit an approximate distribution equation for the unknown boundary conditions, which is in the form of an exponential function.

[0029] In a specific embodiment, the partial differential governing equations and boundary conditions are expressed as follows: (7) (8) Due to the linear nature of the governing equations and boundary conditions, the analytical solution of equation (7) can be decomposed into six parts, which are expressed as follows: (9) in , , , , as well as It satisfies the following equation.

[0030] (10) Based on equation (8), For example: (11) By introducing a variable X ( x ), Y ( y )as well as Z ( z The three functions of ) h 1( x, y, z The solution function is as follows: (12) Substituting equation (12) into (11), the following equation can be obtained: (13) Based on equation (13), the following relationship can be easily obtained: (14) Based on the eigenfunction expansion method and relation (14), the following relational equation can be obtained: (15) (16) in n and m It corresponds to any positive integer.

[0031] Substitute equations (15) and (16) into equation (12), h 1- nm ( x, y, z Any general solution to ) can be obtained as follows: (17) Because equation (12) is a uniform linear partial differential equation, it can be solved by superimposing all... h 1- nm ( x, y, z To obtain h 1( x, y, z The general solution to ) is: (18) Based on boundary conditions f 1( x, y From equations (18) and (19), we can derive: (19) According to equation (19) and the Fourier extended equation, the coefficients Anm This can be represented by equation (20): (20) Similarly, it can be obtained using the same solution method. h 3(x, y, z )and h 4( x, y, z Analytical solution for ) (twenty one) Expansion coefficient Cnm and Dnm The derivation is as follows: (twenty two) It is worth noting that, h 2( x, y, z ), h 5( x, y, z )and h 6( x, y, z The analytical solution is more complex and will be derived in detail in the next section.

[0032] By boundary conditions f 2( x, y ), h 2( x, y, z The derivation is shown in equations (23)-(25). However, f 2( x, y (It is unknown.)

[0033] (twenty three) (twenty four) (25) Based on the eigenfunction expansion method, we can obtain f 2( x, y The analytical solution of ) is given. The partial differential governing equations and boundary conditions are expressed as follows: (26) (27) in f twenty one( x ), f twenty two( x ), f twenty three( y )as well as f twenty four( y ) represents the four boundary conditions of the rectangular region of the seepage field.

[0034] The solution to equation (28) is as follows: (28) in h twenty one( x, y ), h twenty two( x, y ), h twenty three(x, y )as well as h twenty four( x, y The partial differential governing equations and boundary conditions satisfy equations (30a) to (30d). (29) Based on equation (29), h twenty one( x, y For example: (30a) (30b) (30c) (30d) Due to the linear properties of the governing equations and boundary conditions, equation (26) can be regarded as h twenty one( x, y ), h twenty two( x, y ), h twenty three( x, y )as well as h twenty four( x, y The linear superposition of the basic equations in the four equations (30) of ) )

[0035] Based on the principle of eigenfunction expansion, equation (31) in the equation can be used to represent... h twenty one( x, y ), h twenty two( x, y ), h twenty three( x, y )as well as h twenty four( x, y ): (31) Where the expansion coefficient a 2 j , b 2 j , c 2 j as well as d 2 j Provided in equation (32); (32) in f 21 ( x ), f 22 ( x ), f 23 (y )as well as f 24 ( y This is the boundary condition for the second region. Furthermore, j It is the expansion factor. f 21 ( x )and f 23 ( y ) is an unknown condition. f 22 ( x )as well as f 24 ( y The approximate distribution equation of can be obtained through numerical simulation.

[0036] Similarly, this can be achieved by solving equations h 2( x, y, z To obtain the equation h 5( x, y, z ): (33) (34) Enm Integral function f5 ( y, z This can be represented as a piecewise function as follows: (35) The corresponding coefficients a 5 k , b 5 k , c 5 k as well as d 5 k As shown in equation (36), and k It is the expansion factor.

[0037] (36) Because the sixth area has a tunnel surface. h 6( x, y, z The derivation of ) is the most complex. Similar to the previous derivations, h 6( x, y, z The corresponding coefficients of ) Fnm You can obtain: (37) Fnm Integral function f 6( x, zThis can be represented as a piecewise function as follows: (38) in f 6( x, z It can be represented as a linear superposition of the basic equations.

[0038] (39) The corresponding coefficients a 6 u , b 6 u , c 6 u ,and d 6 u As shown in equation (40), and u This represents the expansion coefficient.

[0039] (40) Therefore, the general solution of partial differential equation (9) is as follows: (41) It is worth noting that when analyzing the head distribution at the boundary of the seepage field, the model should be degenerated into two dimensions. This is a very special case.

[0040] Based on the Laplace equation, equation (1) can be obtained when the anisotropic permeability is constant.

[0041] (1) If the permeability is isotropic, i.e. k x =k y =k z Then it becomes the Laplace governing equation: (2) Solving the Laplace equation requires making some assumptions and simplifications to the seepage problem, so that the water head distribution of groundwater in front of the excavation face can be obtained.

[0042] First, the seepage state before the excavation face is assumed to be a steady-state hydraulic head field, and the strata are homogeneous and isotropic. Second, an impermeable boundary and a fixed pressure head are assumed for both the tunnel lining and the tunnel excavation face. h F Assume the water head at the far-field boundary of the ground is equal to the initial elevation of the groundwater level. h 0. Furthermore, assume the initial elevation of the groundwater level. hThere is sufficient surface and groundwater recharge. The effective range of water head distribution in front of the excavation face can be represented by a cuboid.

[0043] For f(y, z), the seepage boundary condition can be represented by a rectangular region, such as... Figure 2 As shown in Equation 3, the mathematical expression for each boundary condition is given. Similar to the analysis method for the second zone, the seepage boundary condition for the fifth zone can also be described as a rectangular region, as shown in Equation 3. Figure 3 As shown in Equation 4, the mathematical expressions for each boundary condition are given.

[0044] (5) (35) It is worth noting that the boundary conditions in the seepage field calculation formula need to be limited to the condition of being within the range of 1 / 2 ≤ ... y, z The coordinates are respectively ( l 1+r, l Within the circular region of 2+r), ​​the water head is 0, where r is the radius of the boulder.

[0045] The corresponding coefficients ak , bk , ck as well as dk As shown in equation (36), and k It is the expansion factor.

[0046] (36) To obtain an explicit solution for the fifth region, numerical simulation should be used. f 2( y )and f 4( z Boundary conditions for the approximate functional equation of ).

[0047] To study the distribution characteristics of groundwater seepage field in the strata in front of the excavation face and the approximate distribution equation under unknown boundary conditions, finite difference software was used to simulate and analyze the seepage in front of the tunnel excavation face under the condition of isolated boulders.

[0048] A computing system for implementing the method includes: a model building module for establishing a three-dimensional geometric model by taking half a cross section based on symmetry, and defining a coordinate system with x, y, and z axes; The first calculation module is used to obtain the two-dimensional head expressions for the six regions based on Darcy's law and boundary conditions; The second calculation module is used to calculate the analytical solution of the head in the three-dimensional seepage field, and to calculate the analytical solution of the head at any position in the three-dimensional seepage field in front of the excavation face.

[0049] Example 1: To study the distribution characteristics of groundwater seepage field in the strata before excavation and the approximate distribution equation under unknown boundary conditions, finite difference software was used to simulate and analyze the seepage.

[0050] According to existing research, when the stratum permeability is higher than 10... -7 ~10 -6 When the excavation speed is ≤0.1~1.0 m / s, the stratum in front of the excavation face can be considered as a drainage condition. Studies on seepage at the tunnel excavation face show that when the excavation speed is <500 m / s and the stratum permeability is >10... -6 At m / s, the numerical analysis of ordinary steady current can obtain values ​​close to the true values ​​[70, 133].

[0051] Considering the symmetry of the three-dimensional seepage field before excavation, the model only shows half of the circular tunnel longitudinally cut along the central axis. The longitudinal and transverse lengths of the model are 8 times and 4 times the tunnel diameter, respectively (8... D and 4 D To focus on analyzing the seepage field before the excavation face, a simplified single-step excavation scheme was adopted to simulate the excavation process, with a fixed displacement of the tunnel perimeter. In the numerical simulation, four tunnels were excavated in one step. D The total height of the model is C +5 D 3 D The model was designed using a non-uniform mesh. The boundary conditions for the numerical model were set as follows: the tunnel lining was impermeable, and the groundwater level was set to be measured from the tunnel arch. h w The groundwater level is assumed to be constant. The table below provides the results through numerical simulation. D =10m and h w / D Approximate distribution equation for unknown boundary conditions = 1-4.

[0052] Remark: Δh = h 0 -hF. The head distribution results obtained from the approximate distribution equation were compared with the results obtained from numerical simulation. f 22 ( x )and f 24 ( y Almost unaffected h w / D The impact. In x =0 and y At point =0, along the vertical surface of the arch, the seepage head distribution is... f 54u( z ) h w / D Increase. h w / D The larger, x =0 and y The faster the seepage head at =0, the more... z The more coordinates are increased, the faster the initial groundwater level is restored. The seepage head obtained through the approximate distribution equation agrees well with the numerical simulation results. For other water level conditions in actual engineering projects, interpolation methods can be used to obtain approximate distribution functions under different boundary conditions.

[0053] The head distribution results obtained from the approximate distribution equation were compared with those obtained from numerical simulation. The seepage head obtained by the approximate distribution equation agrees well with the numerical simulation results.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions, characterized in that, include: S1: A three-dimensional geometric model of the seepage field around the tunnel excavation face is established with the vertical direction as the z-axis, the direction perpendicular to the tunnel excavation as the x-axis, and the direction along the tunnel excavation as the y-axis. S2: Combining the boundary conditions of each region of the seepage field, based on the three-dimensional geometric model of the cuboid, establish the two-dimensional head expressions for the six face regions of the three-dimensional geometric model; S3: Used to construct linear partial differential control equations and Fourier series expansion equations using the continuity conditions between regions, and solve them to obtain the three-dimensional head expressions for the six regions; S4: Based on the superposition of Fourier series, the analytical solution of the water head at any position in the three-dimensional seepage field in front of the excavation face is obtained.

2. The method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions as described in claim 1, is characterized in that, In step S1, the three-dimensional geometric model is set as follows: The seepage state in front of the excavation face is a steady-state hydraulic head field, and the strata are homogeneous and isotropic; The tunnel lining and tunnel excavation face are impermeable boundaries with fixed pressure head h. F ; The water head at the far-field boundary of the ground is equal to the initial elevation h0 of the groundwater level; The initial elevation h0 of the groundwater level has sufficient surface groundwater recharge.

3. The method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions as described in claim 1, is characterized in that... Step S2 includes: S21: The two-dimensional head expression for the six regions of the three-dimensional geometric model of the cuboid is as follows: in f 1( x, y ), f 2( x, y ), f 3( y, z ), f 4( x, z ), f 5( x, y )and f 6( x, z ) represents the expression for the boundaries of the six regions. f 6r (x, z) represents the semicircular boundary of the sixth face. f 6R (x, z) represents the region of the sixth face excluding the semicircle; f 1( x, y ), f 3( y, z )and f 4( x, z ) are known conditions; f 1( x, y ), f 3( y, z )and f 4( x, z ) are the water head at the far-field boundary of the land surface, both defined by h0; D The diameter of the shield excavation face. L 1 represents the boundary length perpendicular to the tunnel boring direction. L 2 represents the boundary length along the tunnel boring direction; S22: Solve f 2( x, y The expression for ) is given, and then substituted into the two-dimensional head expression; S23: Solve f 5( x, y The expression for ) is given, and then substituted into the two-dimensional head expression; S24: Solve f 6( x, z The expression is given, and then substituted into the two-dimensional head expression.

4. The method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions as described in claim 3, is characterized in that... In S22, for f 2( x, y The seepage boundary conditions are represented by a rectangular region, and the mathematical expression for each boundary condition is as follows: Where f 21 ( x )and f 23 ( y The given boundary conditions are: initial groundwater level and seepage head far from the excavation face, both equal to... h 0; Boundary conditions are fitted using approximate functional equations derived from numerical simulation. f 22 ( x )and f 24 ( y ),in f 21 ( x ), f 22 ( x ), f 23 ( y )as well as f 24 ( y ) are the boundary expressions for the two-dimensional region surfaces.

5. The method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions as described in claim 3, is characterized in that, In S23, for f 5( x, y The seepage boundary conditions are represented by a rectangular region, and the mathematical expression for each boundary condition is as follows: The corresponding coefficients a 5k , b 5k , c 5k as well as d 5k As shown below, and k It is the expansion factor; ； f 52 ( y )and f 54 ( z The value was determined through numerical simulation.

6. The method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions as described in claim 3, is characterized in that... In S24, f 6( x, z The seepage boundary conditions are represented by a rectangular region, and the mathematical expression for each boundary condition is as follows: f 62 ( x )and f 64 ( z This was obtained through numerical simulation.

7. The method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions as described in claim 3, is characterized in that, Step S3 includes: S31: Construct the partial differential governing equations: , , , ; S32: The analytical solution of the partial differential governing equation is expressed as: ； in , , , , , These are the boundary expressions for the six faces of the three-dimensional region; S33: Yes , , , , , Solving for each, we get: in, 。 8. The method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions according to any one of claims 4-6, characterized in that, The numerical simulation process includes: Establish a three-dimensional finite difference numerical model; Based on the steady-state seepage assumption, the Laplace equation is solved using finite difference software, the head data of unknown boundary conditions are recorded, and parametric analysis is performed for different water level ratios. Using numerical simulation results, an approximate distribution equation for unknown boundary conditions is fitted, which is in the form of an exponential function.

9. A system for implementing the method for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions as described in any one of claims 1-8, characterized in that, include: The model building module is used to create a three-dimensional geometric model by taking half a cross section based on symmetry, and to define a coordinate system with the x, y, and z axes; The first calculation module is used to obtain the two-dimensional head expressions for the six regions based on Darcy's law and boundary conditions; The second calculation module is used to calculate the analytical solution of the head in the three-dimensional seepage field, and to calculate the analytical solution of the head at any position in the three-dimensional seepage field in front of the excavation face.

Images