An analytical method, system, and medium for steady-state seepage in a layered soil foundation pit

Abstract

The application discloses a layered soil foundation pit steady seepage analytic method, system and medium, based on the steady seepage Darcy law, the seepage field around the foundation pit is divided into three regular regions, the non-homogeneous equation group is constructed by using the region continuous condition and the orthogonality of the Fourier series to solve the seepage field distribution inside and outside the foundation pit, and the analytic solution of the hydraulic head of the layered soil is obtained. The analytic solution of the hydraulic head of the layered soil is simple in form, high in precision, convenient and applicable, fills the blank of the current analytic research on the seepage of the layered soil of the foundation pit, reveals the distribution law of the seepage field inside and outside the foundation pit, and is very meaningful for the application of the foundation pit engineering.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rail transit engineering, and in particular to a layered soil foundation pit steady seepage analytical method, system and medium. BACKGROUND

[0002] In recent years, with the development of large-scale building foundation pits and underground engineering in China, many problems in the design and calculation of supporting structures have gradually emerged. Groundwater seepage control is an important safety control technology in foundation pit engineering.

[0003] In foundation pit engineering, when there is a water head difference inside and outside the foundation pit, groundwater seepage occurs, causing changes in water pressure and effective stress around the foundation pit, affecting the distribution of water and soil pressure on the retaining structure. Groundwater seepage can also cause piping and soil flow accidents in the foundation pit, so the calculation of the foundation pit seepage field is very important.

[0004] Currently, there are analytical solutions for two-dimensional seepage in single-layer soil foundation pits, but in actual engineering, there are rarely only single-layer soil conditions in foundation pits, and layered soil seepage is more close to actual engineering. The analytical solution of single-layer soil seepage is not suitable for actual layered soil engineering, and the analytical solution of layered soil seepage is very difficult to solve, and the solving process is very complex. For two-dimensional seepage problems in layered soil foundation pits, numerical methods such as finite elements and finite differences are mostly used for analysis, and there are few analytical solutions. SUMMARY

[0005] The technical problem to be solved by the present application is to overcome the shortcomings of the prior art and provide a layered soil foundation pit steady seepage analytical method, system and medium.

[0006] To solve the above technical problems, the present application adopts the following technical solutions:

[0007] A layered soil foundation pit steady seepage analytical method, comprising the following steps:

[0008] Step S1: dividing the seepage field around the foundation pit into three regular areas with the foundation pit retaining wall and the wall bottom horizontal line as the boundary, and establishing a two-dimensional calculation model of the anisotropic layered soil layer in the foundation pit;

[0009] The steady seepage balance equation under the two-dimensional calculation model of the foundation pit is:

[0010]

[0011]

[0012]

[0013] In the above formula, H ① j ,H② l H ③ r H ① xj H ② xl H ③ xr H ① zj H ② zl H ③ zr H

[0014] Step S2: based on Darcy's law, assuming that the seepage of each region layered soil layer satisfies two-dimensional seepage balance equation, applying separation of variables method and boundary conditions of each region, obtaining the expression of water head distribution of the foundation pit layered soil;

[0015] Step S3: using the continuity condition between regions and the orthogonality of Fourier series to construct a non-homogeneous equation group, solving the constant term and series term coefficients contained in the water head distribution expression, substituting into the water head distribution expression, obtaining the simplified solution of the water head inside and outside the foundation pit.

[0016] As a further improvement of the above technical solution:

[0017] In the step S2, the expression of the boundary condition of each region is respectively:

[0018] The expression of the boundary condition of the first region is:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] In the above formula, d1 is the distance from the impermeable layer to the water level outside the foundation pit, L eS is the distance from the retaining wall to the impermeable boundary outside the foundation pit, and h is the height of the retaining wall. zj represents the z-direction coordinate of the jth layer of soil in the first region.

[0025] Expression of the boundary condition of the second region:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] In the above formula, d1 represents the distance from the impermeable layer to the top of the foundation pit, d2 represents the distance from the impermeable layer to the bottom of the foundation pit, z1 represents the z-direction coordinate of the lth layer of soil in the second region.

[0032] Expression of the boundary condition of the third region:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] In the above formula, z1 represents the z-direction coordinate of the rth layer of soil in the third region.

[0039] In the step S2, the expression of the water head distribution of the layered soil in the foundation pit is in the form of an explicit series solution, which is respectively:

[0040] The expression of the water head distribution of the layered soil in the foundation pit in the first region is:

[0041]

[0042] wherein, hj is the water head of the jth layer in the first region, D j , E j is a constant term to be solved, D nj , E nj is a series term to be solved,

[0043] The expression for the distribution of water head in the stratified soil of the foundation pit within the second region is:

[0044]

[0045] in, F represents the water head of the l-th layer in the second region. l G l F is the coefficient to be determined for the constant term. ml G ml The coefficients of the series terms are to be determined.

[0046] The expression for the distribution of water head in the stratified soil of the foundation pit within the third region is:

[0047]

[0048] in, J represents the water head of the r-th layer in the third region. r J is the coefficient to be determined for the constant term. ir and U ir The coefficients of the series terms are to be determined.

[0049] In step S3, the relationships between the parameters are derived using the continuity condition between regions and the orthogonality of the Fourier series:

[0050] The condition for continuous inter-regional seepage is:

[0051]

[0052]

[0053]

[0054]

[0055] The relationship between the parameters is as follows:

[0056]

[0057]

[0058]

[0059] Where, α J This represents the relationship between the constant term and the parameter to be determined between the first and second soil layers in the first region, α. nJ This represents the relationship between the exponential term parameters to be determined between the j-th soil layer and the (j+1)-th soil layer in the first region, β. 2L This represents the relationship between the constant term and the parameter to be determined between the first and second soil layers in the second region, β. mLχ represents the relationship between the unknown parameters of the exponential term between the l-th soil layer and the (l+1)-th soil layer in the second region. iR The relationship between the exponential parameters to be determined between the r-th soil layer and the (r+1)-th soil layer in the third region is obtained from the inter-regional seepage continuity condition.

[0060] Determine the constant term D using the definition of a Fourier series. J F L J R D J F L J R The expression is:

[0061]

[0062]

[0063]

[0064] The non-homogeneous equation system was solved by using Gaussian elimination. The coefficients of the constant term and the coefficients of the series term were substituted into the head distribution expression to obtain a simplified solution for the head inside and outside the foundation pit.

[0065] As a general inventive concept, the present invention also provides a steady-state seepage analysis system for layered soil foundation pits, comprising:

[0066] The first module is used to divide the seepage field around the foundation pit into three regular regions with the retaining wall and the horizontal line at the bottom of the wall as the boundary, and to establish a two-dimensional calculation model of the foundation pit in anisotropic stratified soil layers.

[0067] The steady-state seepage equilibrium equation under the two-dimensional calculation model of the foundation pit is:

[0068]

[0069]

[0070]

[0071] In the above formula, H ① j H ② l H ③ r These represent the total water head for the first, second, and third regions, respectively. The calculation reference surface is the bottom surface of the soil layer, k ① xj ,k ② xl ,k ③ xr Let k be the x-direction permeability coefficient of the stratified soil in the first, second, and third regions, respectively.① zj ,k ② zl ,k ③ zr , respectively, are the z-direction permeability coefficients of the stratified soil in the first, second, and third regions, where x represents the horizontal distance from any point in the foundation pit to the retaining wall, and z represents the vertical distance from any point in the foundation pit to the horizontal line at the bottom of the wall;

[0072] The second calculation module is used to obtain the expression for the water head distribution of the stratified soil in the foundation pit based on Darcy's law, assuming that the seepage of the stratified soil layers in each region satisfies the two-dimensional seepage equilibrium equation, and applying the method of separation of variables and the boundary conditions of each region.

[0073] The third calculation module is used to construct a non-homogeneous system of equations by utilizing the continuity conditions between regions and the orthogonality of Fourier series, solve the constant terms and series terms contained in the head distribution expression, and substitute them into the head distribution expression to obtain a simplified solution for the head inside and outside the foundation pit.

[0074] As a general inventive concept, the present invention also provides a steady-state seepage analysis system for layered soil foundation pits, including a microprocessor and a memory interconnected thereto, the microprocessor being programmed or configured to perform the steps of the aforementioned steady-state seepage analysis method for layered soil foundation pits.

[0075] As a general inventive concept, the present invention also provides a computer-readable storage medium storing a computer program programmed or configured to execute the aforementioned analytical method for steady-state seepage in stratified soil foundation pits.

[0076] Compared with the prior art, the advantages of the present invention are as follows:

[0077] This invention, based on Darcy's law of steady-state seepage, divides the seepage field around the foundation pit into three regular regions. It utilizes the continuity of the regions and the orthogonality of Fourier series to construct a non-homogeneous system of equations to solve for the distribution of the seepage field inside and outside the foundation pit. It proposes an analytical solution for the hydraulic head of layered soil foundation pits. This analytical solution for the hydraulic head of layered soil is simple in form, highly accurate, and convenient to apply, filling the gap in current analytical research on seepage in layered soil foundation pits. It further reveals the distribution law of the seepage field inside and outside the foundation pit, which is of great significance for foundation pit engineering applications.

[0078] The analytical solution for the hydraulic head of layered soil foundation pits presented in this invention is universal. To clearly illustrate the analytical solution, the influencing parameters in the head equation (considering the pit width, the distance between the retaining wall and the impermeable layer, the head difference between the inside and outside of the pit, and the influence of soil permeability variations on the seepage distribution) are clearly shown. Furthermore, this invention demonstrates that the permeability distribution of layered soil plays a crucial role in the analysis of the seepage field inside and outside the foundation pit, and the analysis results can provide a reference for foundation pit engineering design and hydraulic engineering practice. Attached Figure Description

[0079] Figure 1 This is a two-dimensional geometric model diagram of the foundation pit;

[0080] Figure 2 The graph shows a comparison between the analytical and numerical solutions.

[0081] Figure 3 This is a diagram showing the total water head distribution around the foundation pit in Embodiment 1 of the present invention. Detailed Implementation

[0082] The present invention will be further described in detail below. Unless otherwise specified, the instruments or materials used in the present invention are commercially available.

[0083] Example 1:

[0084] A method for analyzing steady-state seepage in stratified soil foundation pits includes the following specific steps:

[0085] Step 1: Based on the symmetry, take half section analysis of the foundation pit. Using the foundation pit retaining wall and the horizontal line at the bottom of the wall as the boundary, divide the seepage field around the foundation pit into 3 regular regions and establish a two-dimensional calculation model of the foundation pit in anisotropic layered soil under the support of a suspended impermeable retaining wall.

[0086] The steady-state seepage equilibrium equation under this model is:

[0087]

[0088]

[0089]

[0090] In the above formula, H ① j H ② l H ③ r These represent the total water head for regions ①, ②, and ③, respectively. The reference surface for water head calculation is the bottom surface of the soil layer, k. ① j ,k ② l ,k ③ r These are the anisotropic permeability coefficients of the stratified soil in different regions, k ① xj ,k ② xl ,k ③ xr The x-direction permeability coefficients, k, of the stratified soils in regions ①, ②, and ③ are respectively. ① zj ,k② zl ,k ③ zr Here, represents the z-direction permeability coefficient of the layered soil in regions ①, ②, and ③, respectively; x represents the horizontal distance from any point in the foundation pit to the retaining wall; z represents the vertical distance from any point in the foundation pit to the horizontal line at the bottom of the wall; J represents the number of soil layers on the upper side outside the foundation pit; L represents the number of soil layers on the upper side inside the foundation pit; and R represents the number of soil layers at the bottom of the retaining wall. The foundation pit model is as follows: Figure 1 As shown, h represents the distance from the water level inside the foundation pit to the top of the retaining wall, and i e This indicates that the rate of escape is decreasing.

[0091] Step 2: Based on Darcy's law, the seepage of the stratified soil layers in each region satisfies the two-dimensional seepage equilibrium equation. Using the method of separation of variables and the boundary conditions of each region, the series and expression of the water head distribution of the stratified soil in the foundation pit are written.

[0092] Based on the fundamental assumptions of two-dimensional seepage in the foundation pit and the continuity condition between regions, the boundary conditions of each sub-region can be obtained, and their expressions are as follows:

[0093] Boundary conditions for region ①:

[0094]

[0095] Where d1 is the distance from the impermeable layer to the water level outside the foundation pit, and L e S is the distance from the retaining wall to the impermeable boundary outside the foundation pit, and S is the height of the retaining wall. This represents the z-coordinate of the j-th soil layer in the first region.

[0096] Boundary conditions for region ②:

[0097]

[0098] Where d1 represents the distance from the impermeable layer to the top of the pit, and d2 represents the distance from the impermeable layer to the bottom of the pit. This represents the z-direction coordinate of the l-th soil layer in the second region.

[0099] Boundary conditions for region ③:

[0100]

[0101] in, This represents the z-coordinate of the r-th soil layer in the region;

[0102] The method of separation of variables is used to express the stratified head distribution within a region as a series solution.

[0103] The expression for region ① is:

[0104]

[0105] in, Let D be the head of the j-th layer within region ①. j E j Let D be the coefficient to be determined. nj E nj The coefficients of the series terms are to be determined.

[0106] The expression for region ②:

[0107]

[0108] in, F represents the head of the l-th layer within region ②. l G l Let F be the coefficient to be determined. ml G ml The coefficients of the series terms are to be determined.

[0109] The expression for region ③:

[0110]

[0111] In the above formula, J represents the water head of the r-th layer within region ③. r Let J be the coefficient to be determined. ir and U ir The coefficients for the series terms are to be determined by the seepage continuity conditions of the layered soil in each region;

[0112] Step 3: Construct a non-homogeneous system of equations using the continuity condition between regions and the orthogonality of the Fourier series. Apply the Gaussian elimination method to solve for the constant term and series term coefficients in the head expression. Substitute these coefficients into the equations to obtain the total head distribution inside and outside the pit.

[0113] The continuity condition between regions and the resulting relationships between the parameters are expressed as follows:

[0114] Interval seepage continuity condition:

[0115]

[0116]

[0117] Relationships between parameters:

[0118]

[0119]

[0120]

[0121] Where, α J This represents the relationship between the coefficients to be determined between the first and second soil layers in region ①, α. nJ This represents the relationship between the coefficients to be determined between the j-th soil layer and the (j+1)-th soil layer in region ①. 2L This represents the relationship between the coefficients to be determined between the first and second soil layers in region ②, β. mL χ represents the relationship between the unknown coefficients between the l-th soil layer and the (l+1)-th soil layer in region ①. iR The relationship between the unknown coefficients between the r-th soil layer and the (r+1)-th soil layer in region ③ is obtained from the inter-regional seepage continuity condition.

[0122] Determine the constant term D using the definition of a Fourier series. J ,F L J R Its expression is:

[0123]

[0124]

[0125]

[0126] The above non-homogeneous equation system is solved by using Gaussian elimination. The coefficients of the constant terms and the series terms are then substituted into the analytical expression for the head of the stratified foundation pit. This yields a complete expression for the head inside and outside the foundation pit.

[0127] It should be noted that because the series terms in the equation approach infinity, the solution must be truncated at the Nth term when using MATLAB. This invention uses the sum of the first 20 terms of the analytical solution and verifies it against numerical simulation results, meeting engineering accuracy requirements. A comparison of the analytical and numerical solutions is shown in the figure below. Figure 2 As shown.

[0128] Based on the steady-state seepage analysis method for layered soil foundation pits of the present invention, the foundation pit project of Nanjing Metro DS6 Ningju Line was calculated and analyzed. Table 1 shows the engineering parameters of the foundation pit of Nanjing Metro DS6 Ningju Line, where k1, k2 and k3 are the permeability coefficients of the layered soil layers, and the anisotropy ratio of the engineering permeability is 1.

[0129] Table 1

[0130] Le L d1 [d2] S ​ [caatgcgtaa] [ k3 ] m m m m m -6 cm / s ​ -6 cm / s ​ -6 cm / s ​ 50 12.4 23.44 5.82 21.5 50 30 20

[0131] Based on the specific dimensions and other parameters of the foundation pit for this project, the distribution of the total water head inside and outside the foundation pit after excavation is calculated using the analytical method of this invention, as follows: Figure 3According to the total water head distribution map around the foundation pit project of Nanjing Metro DS6 Ningju Line, the water head line bends at the soil layer interface. When it approaches the bottom of the retaining wall, the total water head on the outside of the retaining wall decreases rapidly, while the total water head on the inside of the retaining wall increases rapidly.

[0132] To prevent seepage damage such as soil erosion and piping in the foundation pit, it is necessary to accurately calculate the outflow gradient I at the excavation face. Analysis of the two-dimensional seepage field in the foundation pit example shows that the seepage path along both sides of the retaining wall is the shortest. Using the analytical solution of this invention, the outflow gradient of the foundation pit in this project is calculated. According to the "Code for Design of Building Foundations" (GB 50007-2011), the results show that the hydraulic gradient at the seepage outlet of this foundation pit project is less than the allowable head gradient, indicating that it is relatively safe.

[0133]

[0134] Where [I] represents the allowable head gradient, I cr The critical head gradient, γ w Where K is the specific weight of water, and K is the safety factor, which is generally taken as 2.0 to 2.5.

[0135] The present invention also provides a steady-state seepage analysis system for layered soil foundation pits, comprising:

[0136] The first module is used to divide the seepage field around the foundation pit into three regular regions with the retaining wall and the horizontal line at the bottom of the wall as the boundary, and to establish a two-dimensional calculation model of the foundation pit in anisotropic stratified soil layers.

[0137] The steady-state seepage equilibrium equation under the two-dimensional calculation model of the foundation pit is:

[0138]

[0139]

[0140]

[0141] In the above formula, H ① j H ② l H ③ r These represent the total water head for the first, second, and third regions, respectively. The calculation reference surface is the bottom surface of the soil layer, k ① xj ,k ② xl ,k ③ xr Let k be the x-direction permeability coefficient of the stratified soil in the first, second, and third regions, respectively. ① zj,k ② zl ,k ③ zr , respectively, are the z-direction permeability coefficients of the stratified soil in the first, second, and third regions, where x represents the horizontal distance from any point in the foundation pit to the retaining wall, and z represents the vertical distance from any point in the foundation pit to the horizontal line at the bottom of the wall;

[0142] The second calculation module is used to obtain the expression for the water head distribution of the stratified soil in the foundation pit based on Darcy's law, assuming that the seepage of the stratified soil layers in each region satisfies the two-dimensional seepage equilibrium equation, and applying the method of separation of variables and the boundary conditions of each region.

[0143] The third calculation module is used to construct a non-homogeneous system of equations by utilizing the continuity conditions between regions and the orthogonality of Fourier series, to solve for the coefficients of the constant terms and series terms contained in the head distribution expression, and to substitute them into the head distribution expression to obtain a simplified solution for the head inside and outside the foundation pit.

[0144] The present invention also provides a steady-state seepage analysis system for layered soil foundation pits, including a microprocessor and a memory interconnected thereto, the microprocessor being programmed or configured to perform the steps of the aforementioned steady-state seepage analysis method for layered soil foundation pits.

[0145] The present invention provides a computer-readable storage medium storing a computer program programmed or configured to execute the aforementioned method for analyzing steady-state seepage in stratified soil foundation pits.

[0146] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of one or more computer-readable storage media (including, but not limited to, disk storage, etc.) containing computer-usable program code. The form of a computer program product implemented on (such as optical memory). This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, produce a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0147] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the present invention, should fall within the protection scope of the present invention.

Claims

1. A method for analyzing steady-state seepage in layered soil foundation pits, characterized in that: Includes the following steps: Step S1: Using the retaining wall and the horizontal line at the bottom of the foundation pit as the boundary, divide the seepage field around the foundation pit into three regular regions and establish a two-dimensional calculation model of the foundation pit in anisotropic stratified soil layers. The steady-state seepage equilibrium equation under the two-dimensional calculation model of the foundation pit is: （1） （2） （3） In the above formula, H ① j , H ② l , H ③ r The total water head represents the first, second, and third regions, respectively, with the bottom surface of the soil layer as the calculation reference. k ① xj , k ② xl , k ③ xr These are the x-direction permeability coefficients of the stratified soil in the first, second, and third regions, respectively. k ① zj , k ② zl , k ③ zr , respectively, are the z-direction permeability coefficients of the stratified soil in the first, second, and third regions, x represents the horizontal distance from any point in the foundation pit to the retaining wall, z represents the vertical distance from any point in the foundation pit to the horizontal line at the bottom of the wall, J represents the number of soil layers on the upper side outside the foundation pit, L represents the number of soil layers on the upper side inside the foundation pit, and R represents the number of soil layers at the bottom of the retaining wall. Step S2: Based on Darcy's law, assuming that the seepage of the stratified soil layers in each region satisfies the two-dimensional seepage equilibrium equation, the separation of variables method and the boundary conditions of each region are applied to obtain the expression for the water head distribution of the stratified soil in the foundation pit. Step S3: Construct a non-homogeneous system of equations using the continuity condition between regions and the orthogonality of Fourier series, solve for the constant term and series term coefficients in the head distribution expression, substitute them into the head distribution expression, and obtain a simplified solution for the head inside and outside the foundation pit. In step S2, the expressions for the boundary conditions of each region are as follows: The expression for the boundary conditions of the first region: In the above formula, The distance from the impermeable layer to the water level outside the foundation pit. This is the distance from the retaining wall to the outer impermeable boundary of the foundation pit. For the height of the retaining wall, This represents the z-coordinate of the j-th soil layer in the first region; The expression for the boundary conditions of the second region: In the above formula, d1 represents the distance from the impermeable layer to the top of the pit, and d2 represents the distance from the impermeable layer to the bottom of the pit. This represents the z-coordinate of the l-th soil layer in the second region; The expression for the boundary conditions of the third region: In the above formula, This represents the z-coordinate of the r-th soil layer in the third region; In step S2, the expression for the layered soil-water head distribution in the foundation pit is in the form of an explicit series solution, as follows: The expression for the distribution of water head in the stratified soil of the foundation pit within the first region is: in, Let the water head be the water head of the j-th layer in the first region. D j , E j The coefficients of the constant term are to be determined. D nj , E nj The coefficients of the series terms are to be determined. ; The expression for the distribution of water head in the stratified soil of the foundation pit within the second region is: in, The water head of the l-th layer in the second region. F l , G l The coefficients of the constant term are to be determined. F ml , G ml The coefficients of the series terms are to be determined. ; The expression for the distribution of water head in the stratified soil of the foundation pit within the third region is: in, For the water head of the r-th layer in the third region, J r The coefficients of the constant term are to be determined. J ir and U ir The coefficients of the series terms are to be determined. .

2. The method for analyzing steady-state seepage in layered soil foundation pits according to claim 1, characterized in that: In step S3, the relationships between the parameters are derived using the continuity condition between regions and the orthogonality of the Fourier series: The condition for continuous inter-regional seepage is: The relationship between the parameters is as follows: in, This represents the relationship between the constant term and the parameter to be determined between the first and second soil layers in the first region. This represents the relationship between the series terms of the parameters to be determined between the j-th soil layer and the (j+1)-th soil layer in the first region. This represents the relationship between the constant term and the parameter to be determined between the first and second soil layers in the second region. This represents the relationship between the undetermined parameters of the series terms between the l-th soil layer and the (l+1)-th soil layer in the second region. The relationship between the series terms of the undetermined parameters between the r-th soil layer and the (r+1)-th soil layer in the third region is obtained from the inter-regional seepage continuity condition. Determine the constant term using the definition of a Fourier series D J , F L , J R , D J , F L , J R The expression is: The non-homogeneous equation system was solved by using Gaussian elimination. The coefficients of the constant term and the coefficients of the series term were substituted into the head distribution expression to obtain a simplified solution for the head inside and outside the foundation pit.

3. A steady-state seepage analysis system for layered soil foundation pits, comprising a microprocessor and a memory interconnected, characterized in that: The microprocessor is programmed or configured to perform the steps of the analytical method for steady-state seepage in stratified soil foundation pits as described in any one of claims 1 to 2.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium contains a computer program that is programmed or configured to perform the steady-state seepage analysis method for stratified soil foundation pits as described in any one of claims 1 to 2.

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