A method and system for calculating the deformation time sequence of a lower tunnel during foundation pit excavation dewatering

Abstract

The present application relates to the technical field of foundation pit engineering and underground tunnel safety protection, especially to a method and system for calculating the deformation time sequence of a tunnel underlying during the excavation and dewatering of a foundation pit. The method is based on the unsteady seepage theory, establishes a model for calculating the drawdown of groundwater level, calculates the drawdown of groundwater level at any dewatering time and at any longitudinal position of the tunnel, calculates the total excavation additional stress at any longitudinal position of the tunnel caused by the unloading of the foundation pit excavation, calculates the dewatering additional stress at any dewatering time and at any longitudinal position of the tunnel in stages, obtains the total additional stress at any dewatering time and at any longitudinal position of the tunnel by using the superposition principle, establishes a longitudinal displacement control equation of the tunnel, and solves the longitudinal displacement control equation of the tunnel to obtain the displacement value at any dewatering time and at any longitudinal position of the tunnel. The present application solves the calculation error problem caused by the traditional method ignoring the time factor, improves the prediction accuracy, and provides a scientific basis for the safe construction of the project.

Description

Technical Field

[0001] This invention relates to the field of foundation pit engineering and underground tunnel safety protection technology, and in particular to a method and system for calculating the deformation time sequence of the tunnel under the foundation pit during excavation and dewatering. Background Technology

[0002] Excavation of foundation pits is a core component of urban underground engineering construction. Pre-dewatering, as a necessary means of dry construction of foundation pits, improves soil stability by lowering the groundwater level and prevents disasters such as quicksand and piping. However, foundation pit dewatering cannot reach the predetermined water level instantly, and the groundwater level fluctuates dynamically over time, causing continuous changes in the additional load borne by adjacent tunnels, resulting in gradual deformation. In severe cases, this can lead to tunnel cracks, leaks, or even ruptures, affecting the normal operation of urban infrastructure.

[0003] Current research on the deformation of adjacent tunnels caused by dewatering in foundation pits largely focuses on the single effect of stable seepage or unloading during foundation pit excavation, failing to provide a systematic coverage of the entire dewatering-deformation process. Existing calculation methods exhibit significant limitations in engineering applicability. These methods often assume that the groundwater level is instantaneously stable, completely ignoring the time effect of the dewatering process and thus failing to accurately capture the dynamic pattern of tunnel deformation as dewatering progresses. Furthermore, they frequently employ simplified soil models such as Winkler foundations or directly ignore soil shear stiffness, resulting in a disconnect from the complex geological conditions in actual engineering projects and significant deviations between calculation results and field conditions. In the calculation of additional loads, the differences in loads at different drawdown stages are not differentiated, further contributing to inaccurate load input.

[0004] In engineering practice, designers often rely on empirical formulas or numerical simulations to predict deformation. However, empirical formulas have large errors and cannot adapt to complex water-bearing strata. Numerical simulations require a lot of modeling time, are difficult to operate, and are difficult to quickly reflect dynamic construction needs.

[0005] Therefore, there is an urgent need for a tunnel deformation calculation method that can take into account the time effect, calculate accurately, and operate easily, to overcome the shortcomings of existing technologies and provide scientific guidance for foundation pit dewatering construction and tunnel protection. Summary of the Invention

[0006] This invention provides a method and system for calculating the time sequence of deformation of the underlying tunnel during foundation pit excavation and dewatering. It effectively solves the calculation error problem caused by neglecting the time factor in traditional methods, improves the accuracy of predicting the deformation of the underlying tunnel during foundation pit dewatering and excavation, and provides a scientific basis for safe construction.

[0007] In a first aspect, the present invention provides a method for calculating the time series deformation of an underlying tunnel during foundation pit excavation and dewatering, including: Based on the theory of unsteady seepage, a groundwater level drawdown calculation model is established to calculate the groundwater level drawdown at any rainfall time and any longitudinal location of the tunnel. Calculate the total additional excavation stress generated at any longitudinal position of the tunnel by the unloading of the foundation pit excavation. Combining the effective stress principle with the groundwater level drawdown calculation model, the additional stress caused by precipitation at any given precipitation time and at any longitudinal location of the tunnel is calculated in stages. The total excavation stress is superimposed with the dewatering stress to obtain the total additional stress at any dewatering time and any longitudinal position of the tunnel. The tunnel is simplified as an infinitely long Euler-Bernoulli beam, and the foundation adopts the Pasternak two-parameter foundation model to establish the longitudinal displacement control equation of the tunnel. Solve the longitudinal displacement control equation of the tunnel to obtain the tunnel deflection equation, and calculate the displacement value at any longitudinal position of the tunnel at any precipitation time.

[0008] This invention enables precise calculation of additional stress from both the excavation unloading and dewatering seepage factors in the foundation pit. It overcomes the limitation of existing steady-state seepage calculations, which can only obtain the final deformation results after the water level stabilizes. It can complete continuous time-series calculation of deformation at any time node and any longitudinal position of the tunnel during foundation pit excavation and dewatering construction. It accurately captures the high-risk stage of rapid settlement growth in the tunnel in the early stage of dewatering. It can provide precise quantitative basis and theoretical support for the safety risk classification and control of the tunnel under the foundation pit during construction, dynamic optimization of construction schemes, and formulation of special protection measures.

[0009] Optionally, the groundwater level drawdown calculation model established based on the unsteady seepage theory, which calculates the groundwater level drawdown at any location along the longitudinal direction of the tunnel for any precipitation time, includes: Based on the theory of unsteady seepage and the assumption of large-diameter incomplete wells, a rectangular foundation pit is equivalent to a circular foundation pit. A calculation model for the groundwater drawdown is established, and the drawdown at any given time and any longitudinal location of the tunnel is obtained. The specific formula is as follows: in, For well functions, , To calculate the distance between the point and the diaphragm wall, , , Let the equivalent radius of the foundation pit be _____. Let the shorter side of the foundation pit be the length. Let the length of the longer side of the foundation pit be . The longitudinal coordinates of the tunnel are: The depth of groundwater level drop outside the diaphragm wall. , , The coefficient of conductivity is 1. Permeability coefficient, For the thickness of the aquifer, is the water storage coefficient of the aquifer.

[0010] This invention solves the core limitation of traditional steady-state seepage calculations in being unable to characterize the dynamic temporal changes in water level, and overcomes the pain point of mismatch between conventional well flow theory and the actual working conditions of dewatering in large-diameter group wells in foundation pits. It lays the core foundation for accurate temporal calculation of additional stress and deformation in subsequent tunnel dewatering.

[0011] Optionally, the calculation of the total additional excavation stress generated at any longitudinal position of the tunnel by the excavation unloading of the foundation pit includes: Based on Mindlin's classical elasticity theory, the additional stress generated at any longitudinal position of the tunnel by vertical unloading at the bottom of the pit and horizontal unloading on the four sidewalls of the pit is calculated respectively, and the total excavation additional stress is obtained by superposition principle.

[0012] This invention enables complete and accurate calculation of the additional stress from the fully unloaded source during foundation pit excavation. It solves the problem that existing technologies often neglect the unloading of side walls, resulting in large deviations in the calculation of additional stress and discrepancies with actual working conditions. This provides complete and reliable stress input support for the accurate calculation of subsequent tunnel excavation deformation.

[0013] Optionally, the method of combining the effective stress principle with the groundwater level drawdown calculation model, based on the relative position of the water level after precipitation and the tunnel axis burial depth, calculates the additional precipitation stress at any longitudinal position of the tunnel at any precipitation time in stages, including: After obtaining the groundwater level drawdown, the additional stress from the precipitation is calculated in two stages based on the relative relationship between the drawdown and the tunnel depth. When the water level is above the tunnel after precipitation ( The additional stress from precipitation is: When some water level remains below the tunnel after precipitation, the additional stress from the precipitation is: When part of the water level drops hour: When part of the water level drops hour: in, The soil weight, The unit weight of saturated soil. It is water-weighted. Precipitation depth For the thickness of the aquifer, This represents the distance between the tunnel axis burial depth and the initial groundwater level. This represents the distance between the initial groundwater level and the ground surface. .

[0014] This invention enables precise time-series calculation of additional stress caused by dewatering at the tunnel location throughout the entire process of foundation pit dewatering. It solves the problem that traditional single-formula calculations cannot adapt to different water level conditions, resulting in large deviations in the calculation of additional stress and discrepancies with the actual stress.

[0015] Optionally, the step of superimposing the total excavation additional stress with the dewatering additional stress to obtain the total additional stress at any dewatering time and any longitudinal position of the tunnel includes: Using the superposition principle, the total additional stress generated by the excavation of the foundation pit at any longitudinal position of the tunnel is superimposed with the additional stress generated by the precipitation at any time and at any longitudinal position of the tunnel, to obtain the total additional stress at any precipitation time and at any longitudinal position of the tunnel under the combined action of foundation pit excavation and precipitation. .

[0016] This invention achieves precise time-sequential synthesis of total additional stress coupled with the dual effects of foundation pit excavation unloading and dewatering seepage, solving the core problem that existing single-factor analysis cannot fully reflect the stress coupling effect throughout the entire foundation pit construction process.

[0017] Optionally, the expression for the longitudinal displacement control equation of the tunnel is: in, This is the foundation reaction coefficient. For the foundation shear modulus, For the elastic modulus of the tunnel, The moment of inertia of the tunnel cross section, The outer diameter of the tunnel. Longitudinal position of the tunnel The total additional stress at the location.

[0018] This invention enables the precise construction of the mechanical control equation for the longitudinal deformation of tunnels under the coupled action of foundation pit excavation and dewatering. It is more in line with the actual collaborative stress characteristics of the tunnel and the surrounding soil, and fully adapts to the time-sequential stress input throughout the construction cycle. It provides a rigorous and reliable mechanical control basis for the analytical solution of deformation at any location and at any dewatering time of the tunnel.

[0019] Optionally, solving the longitudinal displacement control equation of the tunnel to obtain the tunnel deflection equation includes: The tunnel deflection equation is obtained by solving the longitudinal displacement control equation of the tunnel through integral transformation: in, Longitudinal position of the tunnel Total additional stress at the location, The outer diameter of the tunnel. ( This is the foundation reaction coefficient. For the elastic modulus of the tunnel, (moment of inertia of the tunnel cross section). ( (This refers to the shear modulus of the foundation). Longitudinal position of the tunnel Vertical displacement at the location.

[0020] This invention realizes a complete calculation closed loop from additional stress to tunnel deformation, providing a precise and efficient quantitative calculation method for dynamic prediction and safety management of the deformation of the underlying tunnel during foundation pit construction.

[0021] Optionally, the well function Solve using series expansion: .

[0022] This invention enables the engineering-based, high-precision, and rapid solution of unsteady seepage well functions, providing a reliable numerical implementation path for accurately solving the drawdown depth at any time and location throughout the entire dewatering cycle of foundation pits.

[0023] Optionally, the soil weight The stratified averaging method is used to determine the value, and the formula is as follows: in, For the first The natural unit weight of the excavated soil layer. This represents the total number of soil layers involved in the foundation pit excavation. For the first The thickness of the excavated soil layer.

[0024] This invention achieves standardized and unified values ​​for the natural unit weight of multi-layered soil involved in foundation pit excavation, solving the problems of inconsistent unit weight parameters and poor adaptability in multi-layered heterogeneous soil layers.

[0025] On the other hand, the present invention also provides a time-series calculation system for the deformation of an underlying tunnel during foundation pit excavation and dewatering. The system executes the time-series calculation method for the deformation of an underlying tunnel during foundation pit excavation and dewatering provided by the present invention. The system includes an input device, an output device, a processor, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions, and the processor is configured to call the program instructions. The time-series calculation system for the deformation of an underlying tunnel during foundation pit excavation and dewatering provided by the present invention has a compact structure, strong applicability, and greatly improves operating efficiency. Attached Figure Description

[0026] Figure 1 This is a schematic flowchart of a method for calculating the deformation sequence of a tunnel under the foundation pit during dewatering, according to an embodiment of the present invention.

[0027] Figure 2 This is a schematic diagram of the unsteady seepage calculation profile for foundation pit dewatering according to an embodiment of the present invention.

[0028] Figure 3 This is a schematic diagram showing the relative spatial positions of the foundation pit and the underlying tunnel in an embodiment of the present invention.

[0029] Figure 4 This is a schematic diagram illustrating the calculation of additional loads when the water level is above the tunnel, according to an embodiment of the present invention.

[0030] Figure 5 This is a schematic diagram illustrating the calculation of additional loads when a portion of the water level is located below the tunnel, according to an embodiment of the present invention.

[0031] Figure 6 This is a schematic diagram of the Euler-Bernoulli beam-Pasternak foundation calculation model according to an embodiment of the present invention.

[0032] Figure 7 This is a schematic diagram illustrating the variation of the total longitudinal stress of the tunnel over time according to an embodiment of the present invention.

[0033] Figure 8 This is a schematic diagram verifying the tunnel displacement of an embodiment of the present invention with the calculation results of existing research.

[0034] Figure 9 This is a schematic diagram illustrating the variation of the longitudinal displacement distribution of the tunnel over time according to an embodiment of the present invention.

[0035] Figure 10 This is a schematic diagram illustrating the variation of the longitudinal bending moment distribution of the tunnel over time, according to an embodiment of the present invention.

[0036] Figure 11 This is a schematic diagram of a system for calculating the deformation time sequence of a tunnel under the foundation pit during dewatering, according to an embodiment of the present invention. Detailed Implementation

[0037] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0038] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0039] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0040] Please see Figure 1 , Figure 1 This is a flowchart illustrating a method for calculating the deformation time sequence of an underlying tunnel during foundation pit excavation and dewatering, as provided in an embodiment of the present invention. The method includes the following steps: S1. Based on the theory of unsteady seepage, a groundwater level drawdown calculation model is established to calculate the groundwater level drawdown at any time and any location along the longitudinal direction of the tunnel.

[0041] Step S1 is as follows: First, the basic assumptions for the calculation are clarified: the foundation pit is equivalent to a large-diameter incomplete well, the aquifer soil is homogeneous and isotropic, the water head height in the large-diameter well remains consistent, the water flow motion satisfies the Dupuit assumption, and both the water-stopping structure and the bottom of the unconfined aquifer are impermeable media.

[0042] Further, on-site surveys were conducted to determine the physical and mechanical parameters, hydrogeological parameters, and engineering tunnel parameters of the foundation pit, tunnel, and aquifer. A three-dimensional spatial coordinate system was established with the center of the foundation pit as the origin, the tunnel's transverse direction as the X-axis, the tunnel's longitudinal direction as the Y-axis, and the vertical depth direction as the Z-axis.

[0043] Please see Figure 2 , Figure 2 This is a schematic diagram of the unsteady seepage calculation profile for foundation pit dewatering. Based on unsteady seepage theory and the assumption of large-diameter incomplete wells, this invention equates a rectangular foundation pit to a circular one, establishing a groundwater level drawdown calculation model to obtain the groundwater level drawdown at any given dewatering time and any longitudinal location of the tunnel. The specific formula is as follows: in, For well functions, , To calculate the distance between the point and the diaphragm wall, , , Let the equivalent radius of the foundation pit be _____. Let the shorter side of the foundation pit be the length. Let the length of the longer side of the foundation pit be . The longitudinal coordinates of the tunnel are: The depth of groundwater level drop outside the diaphragm wall. , , The coefficient of conductivity is 1. Permeability coefficient, For the thickness of the aquifer, is the water storage coefficient of the aquifer.

[0044] In this embodiment, the groundwater level drawdown calculation considers the influence of the suspended water-stopping structure and applies the dynamic evolution process of the unsteady seepage field, using well functions. Solve using series expansion: .

[0045] When multiple aquifers are involved, the weighted average method is used to calculate the equivalent permeability coefficient. , For the first Aquifer permeability coefficient For the first Thickness of the aquifer.

[0046] S2. Calculate the total additional excavation stress generated at any longitudinal position of the tunnel by the unloading of the foundation pit excavation.

[0047] Please see Figure 3 , Figure 3 This is a schematic diagram showing the relative spatial positions of the foundation pit and the underlying tunnel. Specifically, in this embodiment, based on basic calculation assumptions, the excavation of the soil inside the pit will have an unloading effect on the bottom and surrounding areas of the foundation pit. The soil at the bottom of the foundation pit is subjected to a uniformly distributed unloading load in the upward direction, calculated according to the following formula: Among them, the weight of the excavated soil layer The stratified averaging method is used to determine the value, and the formula is as follows: in, For the first The natural unit weight of the excavated soil layer. This represents the total number of soil layers involved in the foundation pit excavation. For the first The thickness of the excavated soil layer.

[0048] The sidewall of the excavation pit is subjected to a triangular horizontally distributed load, which is: in, The coefficient of earth pressure at rest. The depth of any point on the sidewall of the foundation pit from the ground surface.

[0049] any point at the bottom of the pit unloading at the point The direction is upward. According to Mindlin's classic theory and by integration, the unloading at the bottom of the pit causes any point on the tunnel to be affected. The additional stress at the point is: in, , .

[0050] The additional stresses caused by unloading the four side walls of the foundation pit are as follows: any point on the side wall ① unloading at the point Integrating, we obtain the result at any point on the tunnel caused by the unloading of the sidewall ①. The additional stress at the point is: in, , .

[0051] any point on the side wall ② Any point on the tunnel caused by unloading The additional stress at the point is: in, , .

[0052] Similarly, we can obtain any point on sidewall ③ Any point on the tunnel caused by unloading The additional stress at the point is: in, , .

[0053] any point on the side wall ④ Any point on the tunnel caused by unloading The additional stress at the point is: in, , .

[0054] In summary, using the superposition principle, the total additional excavation stress during foundation pit excavation unloading can be obtained as follows: in, The soil weight, The coefficient of earth pressure at rest. This represents the depth of the calculation point on the sidewall of the foundation pit from the ground surface. This refers to the depth of the foundation pit excavation. The Poisson's ratio of the foundation soil. Let the shorter side of the foundation pit be the length. Let the length of the longer side of the foundation pit be . This refers to the vertical burial depth of the tunnel.

[0055] S3. Combining the effective stress principle with the groundwater level drawdown calculation model, calculate the additional stress caused by precipitation at any precipitation time and at any longitudinal position of the tunnel in stages.

[0056] Specifically, in this embodiment, after obtaining the groundwater level drawdown, the additional stress from the precipitation is calculated in two stages based on the relative relationship between the drawdown and the tunnel depth.

[0057] Please see Figure 4 When the water level is above the tunnel after rainfall ( The additional stress from precipitation is: Please see Figure 5 When some water level remains below the tunnel after precipitation, the additional stress from the precipitation is: When part of the water level drops hour: When part of the water level drops hour: in, The soil weight, The unit weight of saturated soil. It is water-weighted. Precipitation depth For the thickness of the aquifer, This represents the distance between the tunnel axis burial depth and the initial groundwater level. This represents the distance between the initial groundwater level and the ground surface. .

[0058] S4. The total excavation additional stress is superimposed with the precipitation additional stress to obtain the total additional stress at any precipitation time and any longitudinal position of the tunnel.

[0059] Specifically, in this embodiment, the principle of superposition is used to superimpose the total additional stress generated by the excavation of the foundation pit at any longitudinal position of the tunnel with the additional stress generated by the precipitation at any time and at any longitudinal position of the tunnel, to obtain the total additional stress at any precipitation time and at any longitudinal position of the tunnel under the combined action of foundation pit excavation and precipitation. : in, Longitudinal position of the tunnel Total additional excavation stress at the location, Longitudinal position of the tunnel Additional stress from precipitation at the location.

[0060] S5. The tunnel is simplified as an infinitely long Euler-Bernoulli beam, and the foundation adopts the Pasternak two-parameter foundation model to establish the longitudinal displacement control equation of the tunnel.

[0061] Please see Figure 6Specifically, in this embodiment, the tunnel is simplified as an infinitely long Euler-Bernoulli beam, and the foundation soil adopts the Pasternak two-parameter foundation model considering shear stiffness. The tunnel displacement control equation is established by combining the bending theory of the beam and the characteristics of the foundation reaction force: Substituting and simplifying to: in, This is the foundation reaction coefficient. For the foundation shear modulus, For the elastic modulus of the tunnel, The moment of inertia of the tunnel cross section, The outer diameter of the tunnel. Longitudinal position of the tunnel Total additional stress at the location, This is the reaction force of the foundation.

[0062] S6. Solve the longitudinal displacement control equation of the tunnel to obtain the tunnel deflection equation, and calculate the displacement value at any longitudinal position of the tunnel under any precipitation time.

[0063] Specifically, in this embodiment, the tunnel deflection equation is obtained by solving the longitudinal displacement control equation of the tunnel through integral transformation: in, Longitudinal position of the tunnel Total additional stress at the location, The outer diameter of the tunnel. ( This is the foundation reaction coefficient. For the elastic modulus of the tunnel, (moment of inertia of the tunnel cross section). ( (This refers to the shear modulus of the foundation). Longitudinal position of the tunnel Vertical displacement at the location.

[0064] Furthermore, by solving the tunnel deflection equation, the displacement values ​​at any longitudinal location of the tunnel under any precipitation time are obtained. The maximum displacement and impact range of the tunnel were determined, and precipitation parameters and monitoring frequency were optimized.

[0065] Taking the deformation of the existing shield tunnel beneath the Chegongmiao Hub of Shenzhen Metro caused by dewatering of the foundation pit of the Xifeng Road as an example, the technical solution of the present invention will be described in detail.

[0066] The foundation pit project is the Xifeng Road foundation pit of Chegongmiao Hub of Shenzhen Metro. The excavation dimensions of the foundation pit are 23m (length) × 12.5m (width) × 8m (height). It adopts dewatering with a group of manholes and underground continuous wall for water-stopping support. The existing shield tunnel is located directly below the foundation pit and is parallel to the longitudinal direction of the foundation pit. The tunnel segments are made of C50 concrete.

[0067] The core parameters obtained through on-site reconnaissance, geological exploration, and laboratory testing are shown in the table below: Table 1 Calculation Parameter Table (1) Calculation of groundwater level drawdown The water level drawdown at different rainfall times was calculated based on the unsteady seepage formula, and the final groundwater level drawdown at different rainfall times was obtained. The calculation results were completely consistent with the design drawdown in the pit and the on-site water level monitoring data.

[0068] (2) Calculation of additional stress during excavation In this embodiment, the foundation pit is a single homogeneous soil layer. After excavation to the designed pit bottom, the additional stress of the pit bottom unloading at any location of the tunnel is calculated based on the Mindlin rectangular uniformly distributed unloading solution. After superimposing the additional stress contribution of the horizontal unloading of the sidewalls, the total vertical excavation additional stress curve is obtained, as shown below. Figure 7 As shown.

[0069] (3) Calculation of additional stress and total additional stress due to precipitation Tunnel axis burial depth and initial water level distance Based on the relative position of the water level and tunnel depth after dewatering at each construction stage, the additional stress of dewatering at each time node is calculated in two stages, accurately covering the entire process of pre-excavation dewatering and continuous dewatering after excavation.

[0070] The total additional excavation stress generated at the location directly below the center of the longitudinal foundation pit during tunnel excavation. For example, let's illustrate the specific process: ①When t=6 days: steady precipitation depth Calculate the additional stress from dewatering based on the condition that the water level is partially above the tunnel: Additional stress from tunnel dewatering: , Total additional stress: .

[0071] ②When t=9 days: steady precipitation depth Calculate the additional stress from dewatering based on the condition that the water level is above the tunnel: Additional stress from tunnel dewatering: , Total additional stress: .

[0072] ③At t=12 days: steady-state precipitation depth Calculate the additional stress from dewatering based on the condition that the water level is above the tunnel: Additional stress from tunnel dewatering: , Total additional stress: .

[0073] ④At t=15 days: steady-state precipitation depth Calculate the additional stress from dewatering based on the condition that the water level is above the tunnel: Additional stress from tunnel dewatering: , Total additional stress: .

[0074] ⑤At t=18 days: Stable precipitation depth Calculate the additional stress from dewatering based on the condition that the water level is below the tunnel: Additional stress from precipitation inside the tunnel: , Additional stress from precipitation outside the tunnel: , Total additional stress: .

[0075] (4) Establishment and solution of displacement control equations By substituting the parameters, the displacement control equation of the Euler-Bernoulli beam on the Pasternak foundation was established. The tunnel displacement curves at different times were obtained by integral solution, and the maximum displacement of the tunnel and the range of influence were determined.

[0076] (5) Results Analysis The calculation results of this invention are compared with those of traditional analytical methods, numerical calculations, and field measured data. The traditional analytical method uses a differential approach, where the load causes stress at any point on the tunnel axis. displacement for: in, It is far from the endpoint Additional loads acting at the location, The outer diameter of the tunnel. , , The elastic modulus of the tunnel. The moment of inertia of the tunnel cross section, This represents the displacement value of the tunnel. For the bed mass coefficient, This is the shear modulus of the foundation.

[0077] The numerical calculation results are those obtained from simulation software.

[0078] The comparison results are shown in Table 2: Table 2 Comparison of maximum tunnel displacement using different methods (unit: mm) Please see Figure 8 Comparison with Table 2 shows that the error between the calculated values ​​and the measured values ​​in the field using the present invention is only 2.05%, and the calculation accuracy is significantly higher than that of the traditional method. Figure 9 and Figure 10 These are schematic diagrams illustrating the changes in the longitudinal displacement distribution and longitudinal bending moment distribution of the tunnel over time. Figure 9 , 10 It can be seen that as the precipitation time increases, the tunnel's upward displacement gradually decreases and transforms into settlement. Simultaneously, the bending moment gradually decreases with increasing precipitation time, effectively controlling the internal forces generated in the tunnel. This calculation method can accurately calculate the displacement and internal forces of the entire tunnel cross-section at any given time, fully capturing the entire dynamic evolution process. The calculation results are highly consistent with the mechanical mechanism and completely consistent with the actual deformation laws in engineering, verifying the accuracy and engineering applicability of the method.

[0079] Please see Figure 11 In an optional embodiment, the present invention also provides a time-series calculation system for the deformation of an underlying tunnel during foundation pit excavation and dewatering. The system includes an input device, an output device, a processor, and a memory, all interconnected. The memory stores a computer program comprising program instructions, and the processor is configured to invoke the program instructions to execute the specific steps of the aforementioned embodiments of the time-series calculation method for the deformation of an underlying tunnel during foundation pit excavation and dewatering. The time-series calculation system for the deformation of an underlying tunnel during foundation pit excavation and dewatering provided by the present invention has a compact structure, strong applicability, and greatly improves operational efficiency.

[0080] In summary, the present invention provides a method and system for calculating the time-series deformation of tunnels under excavation and dewatering during foundation pit excavation. Its main advantages are that, compared to traditional methods for calculating tunnel deformation under foundation pit dewatering that neglect time effects, use simplified foundation models, rely on complex numerical simulations, and have limited applicability, the present invention innovatively introduces unsteady seepage theory to achieve dynamic calculation of tunnel deformation, accurately capturing the evolution of displacement over time. Simultaneously, relying on the Pasternak two-parameter foundation model considering soil shear stiffness and calculating additional tunnel loads in stages, it significantly improves the consistency between the calculation results and actual working conditions. Furthermore, it directly solves through analytical equations, quickly obtaining tunnel displacement data at any time and location without cumbersome modeling. It combines ease of operation with wide engineering applicability, adapting to various strata such as sand, silt, and soft clay, providing scientific guidance for tunnel protection design in various foundation pit pre-dewatering projects.

[0081] 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 therein. Such 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, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for calculating the time sequence of deformation of an underlying tunnel during foundation pit excavation and dewatering, characterized in that, include: Based on the theory of unsteady seepage, a groundwater level drawdown calculation model is established to calculate the groundwater level drawdown at any rainfall time and any longitudinal location of the tunnel. Calculate the total additional excavation stress generated at any longitudinal position of the tunnel by the unloading of the foundation pit excavation. Combining the effective stress principle with the groundwater level drawdown calculation model, the additional stress caused by precipitation at any given precipitation time and at any longitudinal location of the tunnel is calculated in stages. The total excavation stress is superimposed with the dewatering stress to obtain the total additional stress at any dewatering time and any longitudinal position of the tunnel. The tunnel is simplified as an infinitely long Euler-Bernoulli beam, and the foundation adopts the Pasternak two-parameter foundation model to establish the longitudinal displacement control equation of the tunnel. Solve the longitudinal displacement control equation of the tunnel to obtain the tunnel deflection equation, and calculate the displacement value at any longitudinal position of the tunnel at any precipitation time.

2. The method for calculating the deformation sequence of the underlying tunnel during foundation pit excavation and dewatering according to claim 1, characterized in that, The groundwater level drawdown calculation model, based on the unsteady seepage theory, is established to calculate the groundwater level drawdown at any location along the longitudinal direction of the tunnel for any precipitation time. Based on the theory of unsteady seepage and the assumption of large-diameter incomplete wells, a rectangular foundation pit is equivalent to a circular foundation pit. A calculation model for the groundwater drawdown is established, and the drawdown at any given time and any longitudinal location of the tunnel is obtained. The specific formula is as follows: in, For well functions, , To calculate the distance between the point and the diaphragm wall, , , Let the equivalent radius of the foundation pit be _____. Let the shorter side of the foundation pit be the length. Let the length of the longer side of the foundation pit be . The longitudinal coordinates of the tunnel are: The depth of groundwater level drop outside the diaphragm wall. , , The coefficient of conductivity is 1. Permeability coefficient, For the thickness of the aquifer, is the water storage coefficient of the aquifer.

3. The method for calculating the deformation sequence of the underlying tunnel during foundation pit excavation and dewatering according to claim 1, characterized in that, The total additional excavation stress generated by the unloading of the foundation pit at any longitudinal position of the tunnel includes: Based on Mindlin's classical elasticity theory, the additional stress generated at any longitudinal position of the tunnel by vertical unloading at the bottom of the pit and horizontal unloading on the four sidewalls of the pit is calculated respectively, and the total excavation additional stress is obtained by superposition principle.

4. The method for calculating the deformation sequence of the underlying tunnel during foundation pit excavation and dewatering according to claim 1, characterized in that, The combined effective stress principle and the groundwater level drawdown calculation model, based on the relative position of the water level after precipitation and the tunnel axis burial depth, calculates the additional precipitation stress at any longitudinal position of the tunnel at any precipitation time in stages, including: After obtaining the groundwater level drawdown, the additional stress from the precipitation is calculated in two stages based on the relative relationship between the drawdown and the tunnel depth. When the water level is above the tunnel after precipitation ( The additional stress from precipitation is: When some water level remains below the tunnel after precipitation, the additional stress from the precipitation is: When part of the water level drops hour: When part of the water level drops hour: in, The soil weight, The unit weight of saturated soil. It is water-weighted. Precipitation depth For the thickness of the aquifer, This represents the distance between the tunnel axis burial depth and the initial groundwater level. This represents the distance between the initial groundwater level and the ground surface. .

5. The method for calculating the deformation sequence of the underlying tunnel during foundation pit excavation and dewatering according to claim 1, characterized in that, The step of superimposing the total excavation additional stress with the dewatering additional stress to obtain the total additional stress at any dewatering time and any longitudinal position of the tunnel includes: Using the superposition principle, the total additional stress generated by the excavation of the foundation pit at any longitudinal position of the tunnel is superimposed with the additional stress generated by the precipitation at any time and at any longitudinal position of the tunnel, to obtain the total additional stress at any precipitation time and at any longitudinal position of the tunnel under the combined action of foundation pit excavation and precipitation. .

6. The method for calculating the deformation sequence of the underlying tunnel during foundation pit excavation and dewatering according to claim 1, characterized in that, The expression for the longitudinal displacement control equation of the tunnel is as follows: in, This is the foundation reaction coefficient. For the foundation shear modulus, For the elastic modulus of the tunnel, The moment of inertia of the tunnel cross section, The outer diameter of the tunnel. Longitudinal position of the tunnel The total additional stress at the location.

7. The method for calculating the deformation sequence of the underlying tunnel during foundation pit excavation and dewatering according to claim 1, characterized in that, Solving the longitudinal displacement control equation of the tunnel to obtain the tunnel deflection equation includes: The tunnel deflection equation is obtained by solving the longitudinal displacement control equation of the tunnel through integral transformation: in, Longitudinal position of the tunnel Total additional stress at the location, The outer diameter of the tunnel. ( This is the foundation reaction coefficient. For the elastic modulus of the tunnel, (moment of inertia of the tunnel cross section). ( (This refers to the shear modulus of the foundation). Longitudinal position of the tunnel Vertical displacement at the location.

8. The method for calculating the deformation sequence of the underlying tunnel during foundation pit excavation and dewatering according to claim 2, characterized in that, The well function Solve using series expansion: 。 9. The method for calculating the deformation sequence of the underlying tunnel during foundation pit excavation and dewatering according to claim 3 or 4, characterized in that, The soil weight The stratified averaging method is used to determine the value, and the formula is as follows: in, For the first The natural unit weight of the excavated soil layer. This represents the total number of soil layers involved in the foundation pit excavation. For the first The thickness of the excavated soil layer.

10. A time-series calculation system for deformation of an underlying tunnel during foundation pit excavation and dewatering, characterized in that, The system includes an input device, an output device, a processor, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to call the program instructions to execute the time-series calculation method for deformation of the underlying tunnel during excavation and dewatering as described in any one of claims 1-9.

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