Analytic calculation method for tunnel settlement caused by deep foundation pit dewatering excavation

Abstract

The invention discloses an analytical calculation method for tunnel settlement caused by dewatering excavation of a deep foundation pit, and the method comprises the steps: firstly calculating additional stress caused by pit bottom unloading and side wall unloading of the foundation pit through a Mindlin basic solution, and then determining effective stress increment caused by dewatering in combination with a Dupuit formula and a large well method; and finally, on the basis of a Pasternak foundation-Timoshenko beam coupling model, inputting the total additional stress into a control equation, and solving the vertical displacement of the subway tunnel. By means of the method, additional stress and additional displacement caused by foundation pit excavation and rainfall can be accurately calculated, and therefore accurate prediction of subway tunnel settlement is achieved. Compared with the prior art, the method has the advantages that the coupling effect among multiple factors is comprehensively considered, the limitation of a single-factor analysis method is overcome, and a more scientific and convenient solution is provided especially under complex geological conditions and high underground water level environments.

Description

Technical Field

[0001] This invention relates to the field of underground engineering safety assessment and risk control technology, specifically providing an analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation. Background Technology

[0002] In urban underground space development, deep foundation pit projects face the challenge of controlling settlement of adjacent subway tunnels caused by dewatering of high-water-level strata. Dewatering of foundation pits disrupts the balance between the soil's seepage field and stress field, leading to the dissipation of pore water pressure and an increase in effective stress, which in turn triggers ground consolidation settlement. At the same time, the unloading effect of foundation pit excavation alters the soil stress distribution. The coupling effect of these two factors causes additional deformation of adjacent subway tunnels, seriously threatening their structural safety.

[0003] Existing technologies have the following limitations: most methods only analyze the effects of dewatering or excavation unloading separately, without establishing a unified analytical model for the three factors of pit bottom unloading, sidewall stress release, and dewatering seepage, leading to deviations in the calculation of additional stress; when some schemes convert unloading into equivalent loads, the simplification of retaining constraints and sidewall reduction is insufficient, or additional stress needs to be input externally and then converted into tunnel deformation, which is a lengthy process and depends on intermediate parameters; although numerical simulation methods can reflect the interaction of multiple factors, the modeling is complex and time-consuming, making it difficult to support rapid on-site evaluation and scheme optimization. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides an analytical calculation method for tunnel settlement caused by dewatering excavation in deep foundation pits. This method couples analytical calculation methods for multiple factors, such as bottom unloading, sidewall stress release, and dewatering seepage, to achieve direct calculation from foundation pit construction parameters to tunnel settlement, thereby providing an efficient theoretical tool for engineering decision-making.

[0005] An analytical calculation method for tunnel settlement caused by dewatering excavation in deep foundation pits is proposed. The method first calculates the additional stress caused by unloading at the bottom and sidewalls of the foundation pit using the Mindlin fundamental solution. Then, it combines the Dupuit formula and the well method to determine the effective stress increment caused by dewatering. Finally, based on the Pasternak foundation-Timoshenko beam coupled model, the total additional stress is input into the governing equation to solve for the vertical displacement of the subway tunnel. The calculation steps of the method are as follows: Step 1: Calculate the additional stress caused by unloading at the bottom of the foundation pit; Step 2: Calculate the additional stress caused by unloading the sidewalls of the foundation pit; Step 3: Calculate the additional stress caused by dewatering of the foundation pit; Step 4: Calculate the additional displacement caused by the dewatering excavation of the foundation pit.

[0006] The calculation process for the additional stress caused by unloading at the bottom of the foundation pit in step one is as follows: 1) Calculate the additional stress σ at any point (x0, y0, z0) on the tunnel pipeline caused by unloading at the bottom of the foundation pit based on Mindlin integral solution. z d Its expression is:

[0007] Wherein: the length and width of the rectangular foundation pit are respectively L , B γ represents the soil weight; d ν represents the excavation depth of the foundation pit; ν represents the partial plastic strain. R1 is the distance between any point (ξ, η, d) at the bottom of the pit and any point (x0, y0, z0) on the tunnel pipeline; R2 is the distance between any point (ξ, η, d) at the bottom of the pit and the point symmetric to it about the origin, and any point (x0, y0, z0) on the tunnel pipeline. Integration area D for: .

[0008] The calculation process for the additional stress caused by unloading the sidewall of the foundation pit in step two is as follows: The horizontal triangular unloading loads distributed on the four sidewalls are input into the Mindlin fundamental solution for spatial integration, and the results are superimposed to obtain the total additional stress σ caused by the unloading of the pit sidewalls. Z C ; Among them, the vertical additional stress σ at (x0, y0, z0) on the tunnel caused by unloading of a single sidewall is... Z Ci The expression is:

[0009] Where: K0 is the coefficient of earth pressure at rest; L' is the length of the pit sidewall; ; The integration region C is the sidewall of the foundation pit: .

[0010] The calculation process for the additional stress caused by dewatering of the foundation pit in step three is as follows: Based on the intermittent dewatering model, the equivalent large well method is used to determine the dewatering impact zone. Combining the effective stress principle, the incremental effective stress in the soil caused by dewatering is calculated piecewise, ultimately yielding the additional stress σ caused by dewatering at any point (x0, y0, z0) on the tunnel pipeline. w Z The expression is: Where: H is the initial groundwater head; h0 is the design dewatering level; r0 is the equivalent radius of the foundation pit well; R is the radius of influence of dewatering; γ s γ represents the saturated unit weight of the soil. w It is the density of water.

[0011] The calculation process for the additional displacement caused by the dewatering excavation in step four is as follows: The total additional stress σ in steps one through three Z Input the Pasternak foundation-Timoshenko beam coupled model, and obtain the formula for the additional vertical displacement of the subway tunnel caused by the foundation pit dewatering excavation by analytically solving the governing equations: Where: parameters ; D is the tunnel shear force; E is the tunnel diameter; t I represents the elastic modulus of the tunnel segment. t κ is the tunnel moment of inertia; k is the equivalent section modulus; G is the subgrade coefficient; p G is the shear modulus of the foundation; G is the shear modulus of the tunnel; A is the annular cross-sectional area of ​​the tunnel; ν t The tunnel's Poisson's ratio.

[0012] The foundation pit is a rectangular foundation pit, with a length and width of [missing information]. L , B The excavation depth is d There is a tunnel near the foundation pit, with a diameter of D , burial depth is h The horizontal distance between its axis and the foundation pit is S ; Before excavation, the soil inside the pit exerts a uniformly distributed gravity load downwards on the pit bottom. After the soil is excavated and unloaded, the magnitude of the unloading effect at any point (ξ, η, d) on the pit bottom is: The direction is upward, where γ is the soil weight; According to the Mindlin fundamental solution, the additional stress at any point (x0, y0, z0) on the tunnel pipeline caused by unloading at the bottom of the pit is: Where: ν is the partial plastic strain; R1 is the distance between any point (ξ, η, d) at the bottom of the pit and any point (x0, y0, z0) on the tunnel pipeline; R2 is the distance between the point symmetrical to any point (ξ, η, d) at the bottom of the pit about the origin and any point (x0, y0, z0) on the tunnel pipeline. , .

[0013] The magnitude of the unloading effect at any point (B / 2, η, τ) in sidewall 1 is , direction along x In the negative direction of the axis, the additional vertical stress caused at (x0, y0, z0) on the tunnel pipeline is: in: .

[0014] The magnitude of the unloading effect at any point (ξ, -L / 2, τ) in sidewall 2 is , direction along y In the positive direction of the axis, the additional vertical stress caused at (x0, y0, z0) on the tunnel pipeline is: in: ; The magnitude of the unloading effect at any point (-Β / 2, η, τ) in sidewall 3 is , direction along x In the positive direction of the axis, the additional vertical stress caused at (x0, y0, z0) on the tunnel pipeline is: ; in: ; The magnitude of the unloading effect at any point (ξ, L / 2, τ) in sidewall 4 is , direction along y In the negative direction of the axis, the additional vertical stress caused at (x0, y0, z0) on the tunnel pipeline is: in: ; Calculated using the superposition principle, the vertical additional stress caused by unloading the sidewalls of the foundation pit is: .

[0015] The calculation process for the additional stress caused by the dewatering of the foundation pit is as follows: Based on the Dupuit hypothesis, the formula for calculating the foundation pit dewatering curve is as follows: Where: r0 is the radius of the precipitation well; R is the radius of influence of precipitation, which can be determined by pumping tests or calculated using the Kusakin empirical formula: S w Let be the depth of the precipitation well. For point A, where the water level remains above the calculation point after precipitation, the effective stress change before and after precipitation is: For the case where the water level after precipitation is below point B below the calculation point, the effective stress change before and after precipitation is: Where: σ' A0 σ ' B0 σ represents the effective soil stress at points A and B before precipitation; ' A1 σ ' B1 h0 is the effective soil stress at points A and B after precipitation; h1 is the initial water head depth; h2 is the water head depth after precipitation; h3 is the effective soil stress at points A and B after precipitation. B The burial depth at point B; γ s γ is the saturated unit weight of the soil; γ is the weight of the soil; γ w The specific gravity of water; Combining equations (8) and (9), we obtain the formula for calculating the increase in effective stress caused by precipitation: Where: h0 is the water head depth before precipitation; h is the depth of the calculation point; h1 is the water head depth after precipitation; γ is the soil weight; γ s γ represents the saturated unit weight of the soil. w It is the density of water.

[0016] The project employs a water-stop curtain construction, utilizing the pit's retaining structure and cement mixing walls to form a water-stop curtain that extends downwards to the bedrock and closes around the pit. This provides protection for the pit while isolating it from the hydraulic connection between the inside and outside. The additional stress caused by this method of dewatering is: Among them, S w γ represents the depth of dewatering within the foundation pit, and its magnitude is related to the relative position of the groundwater head within the tunnel and the soil layer after dewatering; s γ is the saturated unit weight of the soil; γ is the weight of the soil; γ w The specific gravity of water; Treating the foundation pit as a large well, for any point (x0, y0, z0) on the tunnel pipeline, when it lies within the equivalent radius r0, i.e. At that time, the water depth inside the pit was S w The design precipitation level h0; when it is outside the equivalent radius r0, i.e. At that time, the water depth inside the pit was S w for: Combining equation (10), for any point (x0, y0, z0) on the tunnel pipeline, the final additional stress caused by the dewatering of the foundation pit is: Where: H is the initial groundwater head; h0 is the design dewatering level; r0 is the equivalent radius of the foundation pit well; R is the radius of influence of dewatering; γ is the soil weight; γ s γ represents the saturated unit weight of the soil. w The specific gravity of water; In summary, during the dewatering excavation process of the foundation pit, the total longitudinal additional stress generated by the unloading of the soil at the bottom of the pit, the unloading of the sidewalls of the foundation pit, and the dewatering inside the foundation pit on the adjacent subway tunnel is: .

[0017] The calculation process for the additional displacement caused by the dewatering excavation of the foundation pit is as follows: Treating the subway tunnel as an infinitely long Timoshenko beam placed on the Pasternak foundation and subject to shear deformation, the governing equation for the tunnel displacement w(x) is obtained as follows: Where: parameters For this governing equation, the analytical solution for the longitudinal deformation of the tunnel, simulated based on the Pasternak foundation beam model, is as follows: in: Integrating, we obtain the deflection equation for the tunnel pipeline as follows: The integration area represents the area affected by foundation pit excavation and dewatering.

[0018] Compared with existing technologies, the analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation of the present invention has the following outstanding advantages: 1) The method of this invention is coupled with multi-factor analytical calculation methods such as pit bottom unloading, sidewall stress release and dewatering seepage, realizing direct calculation from pit construction parameters to tunnel settlement, thereby providing an efficient theoretical tool for engineering decision-making. It solves the problems of existing calculation methods having single consideration factors, complex processes and low accuracy, and can accurately solve the additional stress and additional displacement of adjacent subway tunnel pipelines caused by pit excavation and dewatering.

[0019] 2) The technical advantages of this invention are: it can accurately calculate the additional stress and displacement caused by foundation pit excavation and dewatering, thereby achieving accurate prediction of subway tunnel settlement. Compared with existing technologies, this invention comprehensively considers the coupling effects between multiple factors, overcoming the limitations of single-factor analysis methods. Especially under complex geological conditions and high groundwater levels, it provides a more scientific and convenient solution. This method not only improves the accuracy and reliability of predictions but also provides an efficient calculation tool for practical engineering, possessing significant engineering practical value. It can effectively reduce safety risks caused by settlement during construction and ensure the stability of the tunnel structure. Attached Figure Description

[0020] Figure 1 A top view of the excavation of the adjacent tunnel foundation pit; Figure 2 This is a front view of the excavation of the adjacent tunnel foundation pit; Figure 3 Precipitation curve of the submerged well; Figure 4 A schematic diagram for calculating the effective stress increment caused by precipitation; Figure 5 This is a schematic diagram of intermittent precipitation. Figure 6 A schematic diagram of the large-well method; Figure 7 This is a comparison chart showing the analytical results and the numerical simulation results. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0022] The calculation process for the additional stress caused by the dewatering of the foundation pit is as follows: like Figure 3 As shown, based on the Dupuit assumption, the formula for calculating the foundation pit dewatering curve is as follows: Where: r0 is the radius of the precipitation well; R is the radius of influence of precipitation, which can be determined by pumping tests or calculated using the Kusakin empirical formula: S w The depth of the dewatering well can also be determined by selecting empirical values ​​based on factors such as rock strata properties and particle size. like Figure 4 As shown, for two calculation points A and B, the dashed lines represent the water levels before and after rainfall. The analysis and calculation are carried out using calculation points A and B as examples. If the water level remains above the calculation point after rainfall, that is... Figure 4 The effective stress change at point A before and after precipitation is as follows: If the water level after precipitation is below the calculation point, that is... Figure 4 In the case of point B, the effective stress change before and after precipitation is as follows: Where: σ ' A0 σ ' B0 σ represents the effective soil stress at points A and B before precipitation; ' A1 σ ' B1 h0 is the effective soil stress at points A and B after precipitation; h1 is the initial water head depth; h2 is the water head depth after precipitation; h3 is the effective soil stress at points A and B after precipitation. B The burial depth at point B; γ s γ is the saturated unit weight of the soil; γ is the weight of the soil; γ w The specific gravity of water; Combining equations (8) and (9), we obtain the formula for calculating the increase in effective stress caused by precipitation: Where: h0 is the water head depth before precipitation; h is the depth of the calculation point; h1 is the water head depth after precipitation; γ is the soil weight; γ s γ represents the saturated unit weight of the soil. w It is the density of water.

[0023] In practical engineering, the most common method is to construct a water-stop curtain. This involves using the retaining structure of the foundation pit and cement mixing walls to form a water-stop curtain that extends downwards to the bedrock and closes around the foundation pit. This provides protection for the pit while isolating it from the hydraulic connection between the inside and outside. Figure 5 As shown; From Equation 8, the additional stress caused by precipitation in this manner is: Among them, S w γ represents the depth of dewatering within the foundation pit, and its magnitude is related to the relative position of the groundwater head within the tunnel and the soil layer after dewatering; s γ is the saturated unit weight of the soil; γ is the weight of the soil; γ w The specific gravity of water; Treating the foundation pit as a large well, for any point (x0, y0, z0) on the tunnel pipeline, when it lies within the equivalent radius r0, i.e. At that time, the water depth inside the pit was S w The design precipitation level h0; when it is outside the equivalent radius r0, i.e. At that time, the water depth inside the pit was S w for: Combining equation (10), for any point (x0, y0, z0) on the tunnel pipeline, the final additional stress caused by the dewatering of the foundation pit is: Where: H is the initial groundwater head; h0 is the design dewatering level; r0 is the equivalent radius of the foundation pit well; R is the radius of influence of dewatering; γ is the soil weight; γ s γ represents the saturated unit weight of the soil. w The specific gravity of water; In summary, during the dewatering excavation process of the foundation pit, the total longitudinal additional stress generated by the unloading of the soil at the bottom of the pit, the unloading of the sidewalls of the foundation pit, and the dewatering inside the foundation pit on the adjacent subway tunnel is: .

[0024] The calculation process for the additional displacement caused by the dewatering excavation of the foundation pit is as follows: Treating the subway tunnel as an infinitely long Timoshenko beam placed on the Pasternak foundation and subject to shear deformation, the governing equation for the tunnel displacement w(x) is obtained as follows: Where: parameters For this governing equation, the analytical solution for the longitudinal deformation of the tunnel, simulated based on the Pasternak foundation beam model, is as follows: in: Integrating, we obtain the deflection equation for the tunnel pipeline as follows: The integration area represents the area affected by foundation pit excavation and dewatering.

[0025] In summary, the formula for the additional vertical displacement of the subway tunnel caused by the excavation and dewatering of the foundation pit can be obtained, which is Equation 16.

[0026] Taking a deep foundation pit project in Wuhan as an example, such as Figure 1 , 2 As shown, the excavation pit has a length L=20m, a width B=10m, an excavation depth h=8m, an initial groundwater level of -4m, and a subway tunnel adjacent to the pit. The relevant parameter values ​​are shown in Table 1, and the specific parameters and values ​​of the site soil are shown in Table 2.

[0027] Using Mathematica software to program and calculate Equation 16, the curve of tunnel settlement variation along the tunnel extension direction is obtained as follows: Figure 7 As shown. Furthermore, the embodiment was modeled using Midas GTS NX finite element numerical simulation software. After computational analysis of the model, numerical simulation results were obtained. The vertical displacement of the tunnel arch was extracted, and a curve showing the settlement of the tunnel arch as a function of the tunnel's extension direction was plotted. This curve was then compared with the results obtained from analytical calculations, as shown. Figure 7 As shown.

[0028] Table 1 Tunnel parameters and values

[0029] Table 2 Soil parameters and values

[0030] The calculation results show that the tunnel settlement exhibits a symmetrical nonlinear distribution along the tunnel's extension direction, with larger values ​​in the middle and smaller values ​​at both ends, similar to a normal distribution. In the middle of the tunnel... x At a depth of 50m, the tunnel experiences the greatest settlement, approximately 10.50mm; at both ends of the tunnel, i.e. x =0m and xAt a depth of 100m, the settlement is minimal, approximately 1.85mm. From Figure 7 As can be seen, the analytical calculation results and the numerical simulation results are in good agreement, both exhibiting a symmetrical nonlinear distribution with a larger value in the middle and smaller values ​​at both ends. At the point where the settlement value is largest... x At a depth of 50m, the finite element method (FEM) result is 3% smaller than the analytical solution. This discrepancy arises because the theoretical calculation did not consider the effect of the enclosure structure. x The theoretical calculation results for values ​​in the ranges (0,15) and (85,100) are smaller than expected, mainly because the finite element model does not include a precipitation influence radius, while the theoretical calculation assumes one, and the error is within a reasonable range. Therefore, by comparing the analytical solution with the numerical solution, the correctness and rationality of the analytical solution obtained in this chapter can be verified.

[0031] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solutions of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analytically calculating tunnel settlement caused by dewatering during deep foundation pit excavation, characterized in that, The method first calculates the additional stress caused by unloading at the bottom of the pit and unloading on the sidewalls using the Mindlin basic solution, then determines the effective stress increment caused by dewatering by combining the Dupuit formula and the well method; finally, based on the Pasternak foundation-Timoshenko beam coupled model, the total additional stress is input into the control equation to solve for the vertical displacement of the subway tunnel. The calculation steps of the method are as follows: Step 1: Calculate the additional stress caused by unloading at the bottom of the foundation pit; Step 2: Calculate the additional stress caused by unloading the sidewalls of the foundation pit; Step 3: Calculate the additional stress caused by dewatering of the foundation pit; Step 4: Calculate the additional displacement caused by the dewatering excavation of the foundation pit.

2. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 1, characterized in that, The calculation process for the additional stress caused by unloading at the bottom of the foundation pit in step one is as follows: 1) Calculate the additional stress σ at any point (x0, y0, z0) on the tunnel pipeline caused by unloading at the bottom of the foundation pit based on Mindlin integral solution. z d Its expression is: Wherein: the length and width of the rectangular foundation pit are respectively L , B γ represents the soil weight; d ν represents the excavation depth of the foundation pit; ν represents the partial plastic strain. R1 is the distance between any point (ξ, η, d) at the bottom of the pit and any point (x0, y0, z0) on the tunnel pipeline; R2 is the distance between any point (ξ, η, d) at the bottom of the pit and the point symmetric to it about the origin, and any point (x0, y0, z0) on the tunnel pipeline. Integration area D for: , .

3. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 2, characterized in that, The calculation process for the additional stress caused by unloading the sidewall of the foundation pit in step two is as follows: The horizontal triangular unloading loads distributed on the four sidewalls are input into the Mindlin fundamental solution for spatial integration, and the results are superimposed to obtain the total additional stress σ caused by the unloading of the pit sidewalls. Z C ; Among them, the vertical additional stress σ at (x0, y0, z0) on the tunnel caused by unloading of a single sidewall is... Z Ci The expression is: Where: K0 is the coefficient of earth pressure at rest; L' is the length of the pit sidewall; The integration region C is the sidewall of the foundation pit: .

4. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 3, characterized in that, The calculation process for the additional stress caused by dewatering of the foundation pit in step three is as follows: Based on the intermittent dewatering model, the equivalent large well method is used to determine the dewatering impact zone. Combining the effective stress principle, the incremental effective stress in the soil caused by dewatering is calculated piecewise, ultimately yielding the additional stress σ caused by dewatering at any point (x0, y0, z0) on the tunnel pipeline. w Z The expression is: Where: H is the initial groundwater head; h0 is the design dewatering level; r0 is the equivalent radius of the foundation pit well; R is the radius of influence of dewatering; γ s γ represents the saturated unit weight of the soil. w It is the density of water.

5. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 4, characterized in that, The calculation process for the additional displacement caused by the dewatering excavation in step four is as follows: The total additional stress σ in steps one through three Z Input the Pasternak foundation-Timoshenko beam coupled model, and obtain the formula for the additional vertical displacement of the subway tunnel caused by the foundation pit dewatering excavation by analytically solving the governing equations: Where: parameters ; D is the tunnel shear force; E is the tunnel diameter; t I represents the elastic modulus of the tunnel segment. t κ is the tunnel moment of inertia; k is the equivalent section modulus; G is the subgrade coefficient; p G is the shear modulus of the foundation; G is the shear modulus of the tunnel; A is the annular cross-sectional area of ​​the tunnel; ν t The tunnel's Poisson's ratio.

6. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 2, characterized in that, The foundation pit is a rectangular foundation pit, with a length and width of [missing information]. L , B The excavation depth is d There is a tunnel near the foundation pit, with a diameter of D , burial depth is h The horizontal distance between its axis and the foundation pit is S ; Before excavation, the soil inside the pit exerts a uniformly distributed gravity load downwards on the pit bottom. After the soil is excavated and unloaded, the magnitude of the unloading effect at any point (ξ, η, d) on the pit bottom is: The direction is upward, where γ is the soil weight; According to the Mindlin fundamental solution, the additional stress at any point (x0, y0, z0) on the tunnel pipeline caused by unloading at the bottom of the pit is: Where: ν is the partial plastic strain; R1 is the distance between any point (ξ, η, d) at the bottom of the pit and any point (x0, y0, z0) on the tunnel pipeline; R2 is the distance between the point symmetrical to any point (ξ, η, d) at the bottom of the pit about the origin and any point (x0, y0, z0) on the tunnel pipeline. , .

7. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 3, characterized in that, The magnitude of the unloading effect at any point (B / 2, η, τ) in sidewall 1 is , direction along x In the negative direction of the axis, the additional vertical stress caused at (x0, y0, z0) on the tunnel pipeline is: in: ; The magnitude of the unloading effect at any point (ξ, -L / 2, τ) in sidewall 2 is , direction along y In the positive direction of the axis, the additional vertical stress caused at (x0, y0, z0) on the tunnel pipeline is: in: ; The magnitude of the unloading effect at any point (-Β / 2, η, τ) in sidewall 3 is , direction along x In the positive direction of the axis, the additional vertical stress caused at (x0, y0, z0) on the tunnel pipeline is: ; in: ; The magnitude of the unloading effect at any point (ξ, L / 2, τ) in sidewall 4 is , direction along y In the negative direction of the axis, the additional vertical stress caused at (x0, y0, z0) on the tunnel pipeline is: in: ; Calculated using the superposition principle, the vertical additional stress caused by unloading the sidewalls of the foundation pit is: 。 8. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 4, characterized in that, The calculation process for the additional stress caused by the dewatering of the foundation pit is as follows: Based on the Dupuit hypothesis, the formula for calculating the foundation pit dewatering curve is as follows: Where: r0 is the radius of the precipitation well; R is the radius of influence of precipitation, which can be determined by pumping tests or calculated using the Kusakin empirical formula: S w Let be the depth of the precipitation well. For point A, where the water level remains above the calculation point after precipitation, the effective stress change before and after precipitation is: For the case where the water level after precipitation is below point B below the calculation point, the effective stress change before and after precipitation is: Where: σ ' A0 σ ' B0 σ represents the effective soil stress at points A and B before precipitation; ' A1 σ ' B1 h0 is the effective soil stress at points A and B after precipitation; h1 is the initial water head depth; h2 is the water head depth after precipitation; h3 is the effective soil stress at points A and B after precipitation. B The burial depth at point B; γ s γ is the saturated unit weight of the soil; γ is the weight of the soil; γ w The specific gravity of water; Combining equations (8) and (9), we obtain the formula for calculating the increase in effective stress caused by precipitation: Where: h0 is the water head depth before precipitation; h is the depth of the calculation point; h1 is the water head depth after precipitation; γ is the soil weight; γ s γ represents the saturated unit weight of the soil. w It is the density of water.

9. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 8, characterized in that, The project employs a water-stop curtain construction, utilizing the pit's retaining structure and cement mixing walls to form a water-stop curtain that extends downwards to the bedrock and closes around the pit. This provides protection for the pit while isolating it from the hydraulic connection between the inside and outside. The additional stress caused by this method of dewatering is: Among them, S w γ represents the depth of dewatering within the foundation pit, and its magnitude is related to the relative position of the groundwater head within the tunnel and the soil layer after dewatering; s γ is the saturated unit weight of the soil; γ is the weight of the soil; γ w The specific gravity of water; Treating the foundation pit as a large well, for any point (x0, y0, z0) on the tunnel pipeline, when it lies within the equivalent radius r0, i.e. At that time, the water depth inside the pit was S w The design precipitation level h0; when it is outside the equivalent radius r0, i.e. At that time, the water depth inside the pit was S w for: Combining equation (10), for any point (x0, y0, z0) on the tunnel pipeline, the final additional stress caused by the dewatering of the foundation pit is: Where: H is the initial groundwater head; h0 is the design dewatering level; r0 is the equivalent radius of the foundation pit well; R is the radius of influence of dewatering; γ is the soil weight; γ s γ represents the saturated unit weight of the soil. w The specific gravity of water; In summary, during the dewatering excavation process of the foundation pit, the total longitudinal additional stress generated by the unloading of the soil at the bottom of the pit, the unloading of the sidewalls of the foundation pit, and the dewatering inside the foundation pit on the adjacent subway tunnel is: .

10. The analytical calculation method for tunnel settlement caused by deep foundation pit dewatering excavation according to claim 9, characterized in that, The calculation process for the additional displacement caused by the dewatering excavation of the foundation pit is as follows: Treating the subway tunnel as an infinitely long Timoshenko beam placed on the Pasternak foundation and subject to shear deformation, the governing equation for the tunnel displacement w(x) is obtained as follows: Where: parameters For this governing equation, the analytical solution for the longitudinal deformation of the tunnel, simulated based on the Pasternak foundation beam model, is as follows: Where: parameters Integrating, we obtain the deflection equation for the tunnel pipeline as follows: The integration area represents the area affected by foundation pit excavation and dewatering.

Images