Method and system for analyzing influence of local loading and unloading on deformation of existing shield tunnel

Abstract

The invention provides a method and a system for analyzing influence of local loading and unloading on deformation of an existing shield tunnel, and relates to the field of influence of foundation pit construction on the existing tunnel. The method comprises the steps that shield tunnel vertical additional stress caused by foundation pit excavation is calculated through a Mindlin stress solution; analyzing the influence of the longitudinal axial force on the flexural rigidity and shear rigidity of the circular seam joint, and dividing a joint deformation mode into three stages according to the relative magnitude of the axial force and the bending moment and the vertical displacement between rings; a tunnel displacement control equation is established based on a Winkler foundation model, loop iteration is conducted through a state space method, and the rigidity of a circular seam joint is dynamically adjusted to be matched with the final deformation mode of the circular seam joint; and finally, constructing a prediction system, and outputting a deformation value of the shield tunnel by inputting the number of iterations and parameters of a foundation pit, bolts, concrete and segments. By means of the method, deformation prediction of the existing shield tunnel can be achieved for foundation pit construction, an effective scientific basis is provided for foundation pit engineering construction, the problem that parameter decision of operators on a construction site is difficult is solved, and foundation pit engineering site construction is truly guided.

Description

Technical Field

[0001] The present invention relates to the field of influence of foundation pit construction on existing tunnels, and in particular to a method and system for analyzing influence of local loading and unloading on deformation of existing shield tunnels. Background Art

[0002] With my country's rapid economic development and accelerating urbanization, subways have played a vital role in alleviating traffic pressures in major Chinese cities and have become a vital transportation option for millions of people. However, with the increasing coverage of subway networks and the growing demand for underground space in major cities, excavation of foundation pits above existing subway tunnels is inevitable and even becoming increasingly common. If excavation significantly disturbs the adjacent soil, it will inevitably have a negative impact on the existing subway tunnels, hindering their normal operation.

[0003] Excavation construction inevitably disrupts the previously balanced stress field in the foundation soil, causing stress release and soil rebound in the underlying soil layer. This can lead to a series of structural defects in existing shield tunnels, such as cracking of the segments, joint opening, and uneven longitudinal settlement. For many excavation projects, the disturbed displacement of the underlying subway tunnel is a key factor in determining the success or failure of the excavation. Furthermore, compared to other tunnel construction methods such as immersed tubes and jacking tunnels, the lining structure of shield tunnels is composed of precast reinforced concrete segments connected by bolts. The presence of tunnel joints makes the lining structure discontinuous. Joints are both a critical component and the weakest link in the shield tunnel structure, and their mechanical properties influence and even control the overall response of the lining. Among the structural defects caused by the longitudinal uplift of shield tunnel segments, damage often occurs at the circumferential joints. Therefore, the influence of the circumferential joints in shield tunnels on the overall longitudinal deformation of the tunnel cannot be ignored.

[0004] Therefore, it is particularly important to conduct in-depth research on the impact of foundation pit construction on existing underlying shield tunnels, especially the mechanical properties of girth joints and their influence on overall deformation. Therefore, this invention patent considers the impact of tunnel girth joints on shield tunnel deformation and proposes a more reasonable shield tunnel deformation prediction model. This further explains the deformation patterns and characteristics of existing tunnels caused by foundation pit construction, and improves the safety and stability of foundation pit construction. Summary of the Invention

[0005] Based on the above analysis, the present invention provides a method and system for analyzing the impact of local loading and unloading on the deformation of existing shield tunnels, so as to overcome the shortcomings of the existing technology and achieve accurate prediction of the deformation of existing underlying tunnels caused by foundation pit construction.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions: a method and system for analyzing the effects of local loading and unloading on the deformation of an existing shield tunnel, comprising:

[0007] Step 1: Calculate the vertical additional stress in the existing underlying shield tunnel caused by foundation pit excavation using the Mindlin stress solution;

[0008] Step 2: The influence of longitudinal axial force on the bending and shear stiffness of the girth joint was analyzed, and the bending and shear deformation modes of the girth joint were divided into three stages according to the relative magnitude of the axial force and bending moment and the relative vertical displacement between the rings.

[0009] Step 3: On this basis, the tunnel displacement control equation is established based on the Winkler foundation model. The state space method is used to iterate the bending and shear stiffness of the tunnel girth joint, so that the girth joint stiffness can be continuously and dynamically adjusted to match the final deformation mode of the girth joint.

[0010] Step 4: Based on the above theory, a prediction system for the impact of foundation pit construction on shield tunnel deformation is constructed;

[0011] Step 5: Input the number of iterations, foundation pit parameters, bolt parameters, concrete parameters, and segment parameters into the prediction system for the influence of shield tunnel deformation, and output the shield tunnel deformation value.

[0012] Furthermore, the prediction system for the impact of foundation pit construction on shield tunnel deformation is:

[0013] (1) Assuming that the bending stiffness and shear stiffness of the tunnel girth joint are both in the first stage of deformation, the bending moment and relative vertical displacement of each girth joint are obtained according to the initial load conditions.

[0014] (2) The bending moments and relative vertical displacements of the respective circumferential joints calculated in step (1) are compared with their respective deformation modes, and the bending stiffness and shear stiffness of the respective circumferential joints are further updated.

[0015] (3) Substitute the updated bending stiffness and shear stiffness of each girth joint into the tunnel displacement control equation to obtain the new bending moment and relative vertical displacement of each girth joint.

[0016] (4) Repeat processes (2) and (3) until the change values ​​of the bending stiffness and shear stiffness in two adjacent processes meet the effective range.

[0017] Furthermore, the vertical additional stress of the existing underlying shield tunnel caused by foundation pit excavation is calculated by the Mindlin stress solution as follows:

[0018]

[0019] Where: σdξdη is the vertical additional stress in the direction of the tunnel axis caused by the force σdξdη at a point (ξ,η) on the tunnel axis under the rectangular uniformly distributed load at the pit bottom. H is the depth of concentrated force, and υ is the Poisson's ratio of the soil.

[0020] Furthermore, the bending and shear deformation modes of the annular seam joint are divided into three stages:

[0021] Based on the contact state of the annular joint and the position of the neutral axis, the bending deformation at the annular joint of a shield tunnel under the coupling of axial force and bending moment is divided into three deformation modes. The shear deformation is also divided into three deformation modes according to the different stages in which the shear force at the annular joint is shared by the sliding friction resistance of adjacent contact surfaces, the longitudinal bolts, and the tenon and groove.

[0022] Furthermore, the tunnel displacement control equation established based on the Winkler foundation model is:

[0023]

[0024] in,

[0025] Where K is the foundation reaction coefficient, N is the axial force acting on the tunnel structure, EI is the flexural stiffness of the tunnel structure, ω is the displacement of the tunnel structure, θ is the deflection of the tunnel structure, M and Q are the bending moment and shear force along the tunnel axis, and q is the uniformly distributed load acting on the tunnel structure.

[0026] Furthermore, the state space method is used to iterate the bending stiffness and shear stiffness of the tunnel girth joint, so that the girth joint stiffness can be continuously and dynamically adjusted to match the final deformation mode of the girth joint:

[0027] Assuming that the initial tunnel girth joint bending stiffness and shear stiffness are both in the first stage of deformation, the bending moment and shear force of each ring girth joint are calculated according to the continuity conditions of the shield tunnel joint bending moment and shear force. The bending moment and shear force of each ring girth joint are compared with the three-stage critical values ​​of the girth joint bending and shear modes, and the girth joint stiffness of each ring segment is updated. Then, the state variable on the left side of the rightmost shield tunnel girth joint is transferred to the right side through the girth joint, and the state vector is repeatedly transferred from left to right until it reaches the rightmost side.

[0028] Furthermore, the data parameters input into the shield tunnel deformation prediction system for foundation pit construction are:

[0029] Bolt parameters include bolt length, tensile stiffness of inter-ring joint bolts, and distance from bolt to segment centroid; concrete parameters include concrete flexural stiffness and concrete elastic modulus; segment parameters include segment thickness, segment ring width, segment inner diameter, segment outer diameter, and number of segments on one side; foundation pit parameters include soil Poisson's ratio, foundation pit excavation depth, distance from pit centerline to tunnel centerline, pit width, pit length, and soil weight.

[0030] The present invention has the following beneficial effects: it proposes a theoretical calculation method that takes into account the nonlinear variation of tunnel girth joint stiffness. In this system, the bending and shear stiffness of tunnel girth joints can be dynamically adjusted based on the joint's current deformation mode to match the joint's final deformation mode, enabling a more accurate simulation of the mechanical properties of tunnel girth joints. This system thus constructs a more precise prediction system for the impact of foundation pit construction on shield tunnel deformation. This provides an effective scientific basis for foundation pit construction, solves the parameter decision-making difficulties faced by construction site operators, and truly guides on-site foundation pit construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A flow chart of a method and system for analyzing the effect of local loading and unloading on deformation of an existing shield tunnel provided by an embodiment of the present invention;

[0032] Figure 2 A flow chart of a system for predicting the effect of foundation pit construction on shield tunnel deformation provided by an embodiment of the present invention;

[0033] Figure 3 This is a comparison chart of the calculation results of the prediction system for the impact of foundation pit construction on shield tunnel deformation provided by an embodiment of the present invention and the calculation results of other methods. DETAILED DESCRIPTION

[0034] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0035] like Figure 1 As shown, an embodiment of the present invention provides a method and system for analyzing the effect of local loading and unloading on the deformation of an existing shield tunnel, comprising the following steps:

[0036] Step 1: Calculate the vertical additional stress in the existing underlying shield tunnel caused by foundation pit excavation using the Mindlin stress solution;

[0037] Step 2: The influence of longitudinal axial force on the bending and shear stiffness of the girth joint was analyzed, and the bending and shear deformation modes of the girth joint were divided into three stages according to the relative magnitude of the axial force and bending moment and the relative vertical displacement between the rings.

[0038] Step 3: On this basis, the tunnel displacement control equation is established based on the Winkler foundation model. The state space method is used to iterate the bending and shear stiffness of the tunnel girth joint, so that the girth joint stiffness can be continuously and dynamically adjusted to match the final deformation mode of the girth joint.

[0039] Step 4: Based on the above theory, a prediction system for the impact of foundation pit construction on shield tunnel deformation is constructed;

[0040] Step 5: Input the number of iterations, foundation pit parameters, bolt parameters, concrete parameters, and segment parameters into the prediction system for the influence of shield tunnel deformation, and output the shield tunnel deformation value.

[0041] It should be understood that shield tunnel deformation refers to the changes in shape, size or position of the shield tunnel structure caused by external forces, soil changes or other factors during construction or operation; joint stiffness refers to the stiffness characteristics of the tunnel segment at the annular joint, which reflects the ability of the annular joint of the segment to deform under force and external pressure.

[0042] Optionally, the vertical additional stress of the existing underlying shield tunnel caused by foundation pit excavation is calculated by Mindlin stress solution as follows:

[0043]

[0044] Where: σdξdη is the vertical additional stress in the direction of the tunnel axis caused by the force σdξdη at a point (ξ,η) on the tunnel axis under the rectangular uniformly distributed load at the pit bottom. H is the depth of concentrated force, and υ is the Poisson's ratio of the soil.

[0045] It can be explained that vertical additional stress refers to the additional vertical stress applied to a certain part of the soil layer or structure due to factors such as external loads or soil changes. This stress is usually relative to the static stress state under the original geological conditions; Mindlin stress solution is a solution used to describe the stress field generated by point loads or concentrated loads in soil and other continuous media, especially for plane strain or three-dimensional strain conditions.

[0046] Optionally, the tunnel displacement control equation established based on the Winkler foundation model is:

[0047]

[0048] in,

[0049] Where K is the foundation reaction coefficient, N is the axial force acting on the tunnel structure, EI is the flexural stiffness of the tunnel structure, ω is the displacement of the tunnel structure, θ is the deflection of the tunnel structure, M and Q are the bending moment and shear force along the tunnel axis, and q is the uniformly distributed load acting on the tunnel structure.

[0050] It can be explained that the tunnel displacement control equation is a mathematical model used to describe the displacement and deformation caused by factors such as stratum deformation and stress redistribution during the construction or operation of the tunnel.

[0051] Optionally, the state space method is used to iterate the bending stiffness and shear stiffness of the tunnel girth joint so that the girth joint stiffness can be continuously and dynamically adjusted to match the final deformation mode of the girth joint:

[0052] Assuming that the initial tunnel girth joint bending stiffness and shear stiffness are both in the first stage of deformation, the bending moment and shear force of each ring girth joint are calculated according to the continuity conditions of the shield tunnel joint bending moment and shear force. The bending moment and shear force of each ring girth joint are compared with the three-stage critical values ​​of the girth joint bending and shear modes, and the girth joint stiffness of each ring segment is updated. Then, the state variable on the left side of the rightmost shield tunnel girth joint is transferred to the right side through the girth joint, and the state vector is repeatedly transferred from left to right until it reaches the rightmost side.

[0053] It can be explained that the state vector refers to a set of variables used to describe the state of the annular joint of a tunnel (especially a shield tunnel) and the entire tunnel structure at a certain node.

[0054] Optionally, the data parameters input into the shield tunnel deformation prediction system for foundation pit construction are:

[0055] Bolt parameters include bolt length, tensile stiffness of inter-ring joint bolts, and distance from bolt to segment centroid; concrete parameters include concrete flexural stiffness and concrete elastic modulus; segment parameters include segment thickness, segment ring width, segment inner diameter, segment outer diameter, and number of segments on one side; foundation pit parameters include soil Poisson's ratio, foundation pit excavation depth, distance from pit centerline to tunnel centerline, pit width, pit length, and soil weight.

[0056] like Figure 2 As shown in FIG, the prediction system of the influence of foundation pit construction on shield tunnel deformation is:

[0057] (1) Assuming that the bending stiffness and shear stiffness of the tunnel girth joint are both in the first stage of deformation, the bending moment and relative vertical displacement of each girth joint are obtained according to the initial load conditions.

[0058] (2) The bending moments and relative vertical displacements of the respective circumferential joints calculated in step (1) are compared with their respective deformation modes, and the bending stiffness and shear stiffness of the respective circumferential joints are further updated.

[0059] (3) Substitute the updated bending stiffness and shear stiffness of each girth joint into the tunnel displacement control equation to obtain the new bending moment and relative vertical displacement of each girth joint.

[0060] (4) Repeat processes (2) and (3) until the change values ​​of the bending stiffness and shear stiffness in two adjacent processes meet the effective range.

[0061] Combine Figure 1 and Figure 3 In order to ensure the accuracy of the prediction method and system for the impact of foundation pit construction on shield tunnel deformation, this embodiment is based on the N01 foundation pit project on Dongfang Road in Shanghai, which is approximately a rectangular foundation pit with a length of 26m and a width of 18.1m, and an excavation depth of 6.5m. The Shanghai Metro Line 2 upline tunnel passes under the foundation pit, and the two are 45° in plane. The tunnel is buried at a depth of 12.36m, the outer diameter of the tunnel is 6.2m, the lining thickness is 0.35m, the ring width is 1.2m, and the tunnel ring joint is connected by 17 M30 high-strength longitudinal bolts. The actual engineering data parameters are substituted into the shield tunnel deformation prediction model to obtain the shield tunnel deformation value caused by foundation pit construction, which is compared with the measured results as shown below. Figure 3 As shown in the figure, the variation pattern of the system calculation results along the tunnel axis is consistent with the field measurements, confirming the correctness of the calculation theory proposed in this patent. Furthermore, because the calculation method in this paper fully considers the impact of the inter-segment joints on the tunnel, it also proves that the shield tunnel deformation prediction model proposed in this patent can accurately predict the deformation of the underlying existing shield tunnel during foundation pit construction.

Claims

1. A method and system for analyzing the effect of local loading and unloading on the deformation of an existing shield tunnel, characterized in that: The method comprises: Step 1: Calculate the vertical additional stress in the existing underlying shield tunnel caused by foundation pit excavation using the Mindlin stress solution; Step 2: The influence of longitudinal axial force on the bending and shear stiffness of the girth joint was analyzed, and the bending and shear deformation modes of the girth joint were divided into three stages according to the relative magnitude of the axial force and bending moment and the relative vertical displacement between the rings. Step 3: On this basis, the tunnel displacement control equation is established based on the Winkler foundation model. The state space method is used to iterate the bending and shear stiffness of the tunnel girth joint, so that the girth joint stiffness can be continuously and dynamically adjusted to match the final deformation mode of the girth joint. Step 4: Based on the above theory, a prediction system for the impact of foundation pit construction on shield tunnel deformation is constructed; Step 5: Input the number of iterations, foundation pit parameters, bolt parameters, concrete parameters, and segment parameters into the prediction system for the influence of shield tunnel deformation, and output the shield tunnel deformation value.

2. The method and system for analyzing the effect of local loading and unloading on deformation of an existing shield tunnel according to claim 1, characterized in that: The prediction system for the effect of foundation pit construction on shield tunnel deformation is: (1) Assuming that the bending stiffness and shear stiffness of the tunnel girth joint are both in the first stage of deformation, the bending moment and relative vertical displacement of each girth joint are obtained according to the initial load conditions. (2) The bending moments and relative vertical displacements of the respective circumferential joints calculated in step (1) are compared with their respective deformation modes, and the bending stiffness and shear stiffness of the respective circumferential joints are further updated. (3) Substitute the updated bending stiffness and shear stiffness of each girth joint into the tunnel displacement control equation to obtain the new bending moment and relative vertical displacement of each girth joint. (4) Repeat processes (2) and (3) until the change values ​​of the bending stiffness and shear stiffness in two adjacent processes meet the effective range.

3. The method and system for analyzing the effect of local loading and unloading on deformation of an existing shield tunnel according to claim 2, characterized in that: The vertical additional stress of the existing underlying shield tunnel caused by foundation pit excavation is calculated by Mindlin stress solution as follows: Where: σdξdη is the vertical additional stress in the direction of the tunnel axis caused by the force σdξdη at a point (ξ,η) on the tunnel axis under the rectangular uniformly distributed load at the pit bottom. H is the depth of concentrated force, and υ is the Poisson's ratio of the soil.

4. The method and system for analyzing the effect of local loading and unloading on deformation of an existing shield tunnel according to claim 3, characterized in that: The bending and shear deformation modes of the annular joint are divided into three stages: Based on the contact state of the annular joint and the position of the neutral axis, the bending deformation at the annular joint of a shield tunnel under the coupling of axial force and bending moment is divided into three deformation modes. The shear deformation is also divided into three deformation modes according to the different stages in which the shear force at the annular joint is shared by the sliding friction resistance of adjacent contact surfaces, the longitudinal bolts, and the tenon and groove.

5. The method and system for analyzing the effect of local loading and unloading on deformation of an existing shield tunnel according to claim 4, characterized in that: The tunnel displacement control equation established based on the Winkler foundation model is: in, Where K is the foundation reaction coefficient, N is the axial force acting on the tunnel structure, EI is the flexural stiffness of the tunnel structure, ω is the displacement of the tunnel structure, θ is the deflection of the tunnel structure, M and Q are the bending moment and shear force along the tunnel axis, and q is the uniformly distributed load acting on the tunnel structure.

6. The method and system for analyzing the effect of local loading and unloading on deformation of an existing shield tunnel according to claim 5, characterized in that: The state space method is used to iterate the bending stiffness and shear stiffness of the tunnel girth joint, so that the girth joint stiffness can be continuously and dynamically adjusted to match the final deformation mode of the girth joint: Assuming that the initial tunnel girth joint bending stiffness and shear stiffness are both in the first stage of deformation, the bending moment and shear force of each ring girth joint are calculated according to the continuity conditions of the shield tunnel joint bending moment and shear force. The bending moment and shear force of each ring girth joint are compared with the three-stage critical values ​​of the girth joint bending and shear modes, and the girth joint stiffness of each ring segment is updated. Then, the state variable on the left side of the rightmost shield tunnel girth joint is transferred to the right side through the girth joint, and the state vector is repeatedly transferred from left to right until it reaches the rightmost side.

7. The method and system for analyzing the effect of local loading and unloading on deformation of an existing shield tunnel according to claim 6, characterized in that: The data parameters input into the shield tunnel deformation prediction system for foundation pit construction are: Bolt parameters include bolt length, tensile stiffness of inter-ring joint bolts, and distance from bolt to segment centroid; concrete parameters include concrete flexural stiffness and concrete elastic modulus; segment parameters include segment thickness, segment ring width, segment inner diameter, segment outer diameter, and number of segments on one side; foundation pit parameters include soil Poisson's ratio, foundation pit excavation depth, distance from pit centerline to tunnel centerline, pit width, pit length, and soil weight.

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