A method for calculating deformation of adjacent tunnel induced by foundation pit excavation considering spatial effect

Abstract

The application discloses a kind of calculation method of considering space effect's foundation pit excavation induced adjacent tunnel deformation, and the method steps are as follows: (1) determine the three-dimensional curve of lateral deformation of retaining wall;(2) determine the soil unloading caused by the deformation of retaining wall induced by foundation pit excavation;(3) determine the deformation control equation of adjacent tunnel by using Winkler foundation and Timoshenko beam model;(4) determine each parameter to solve the deformation of adjacent tunnel.The method can analyze the response of adjacent tunnel caused by foundation pit excavation, evaluate the safety of tunnel before foundation pit excavation, so as to effectively avoid the accident of adjacent tunnel damage caused by foundation pit excavation.

Description

Technical Field

[0001] This invention relates to the field of underground structure design, and more specifically to a calculation method for the deformation of adjacent tunnels induced by foundation pit excavation, taking into account spatial effects. Background Technology

[0002] Urban subways, with their massive passenger capacity and relatively high operating speed, are increasingly demonstrating their ability to alleviate urban traffic congestion. Therefore, ensuring the safe and stable operation of subways is receiving increasing attention. As the commercial value along subway lines becomes more significant, there are more and more engineering projects involving the construction of adjacent subway tunnels. The loading and unloading caused by construction will lead to additional deformation and internal forces in adjacent tunnels. When these forces accumulate to a certain extent, they will cause various degrees of tunnel damage, such as segment joint opening and water seepage, seriously affecting the safe operation of subway tunnels. Excavation and unloading of the foundation pit will cause stress redistribution in the soil outside the pit, thus affecting the additional deformation and internal forces of adjacent tunnels. Numerous accidents involving damage to adjacent tunnels caused by foundation pit excavation have been reported both domestically and internationally. Therefore, it is necessary to study and analyze the response of adjacent tunnels caused by foundation pit excavation and assess tunnel safety before excavation.

[0003] Research methods for the environmental impact of foundation pit excavation mainly include numerical models and theoretical analysis. Three-dimensional numerical simulation can consider the spatial effects of foundation pit excavation and is relatively consistent with actual working conditions; however, its results depend on the accuracy of parameter selection, and the modeling is complex and computationally time-consuming. Theoretical analytical methods have clear principles and require less computation time, therefore they are often used in studies on the environmental impact of foundation pit excavation. However, existing theoretical methods use stress release coefficients to represent the magnitude of unloading induced by foundation pit excavation, and these stress release coefficients are fixed values. Due to the deformation of the retaining structure caused by foundation pit excavation, the lateral earth pressure outside the pit gradually changes from static earth pressure to active earth pressure, and its magnitude is closely related to the deformation of the retaining structure. Furthermore, due to the spatial effects of foundation pit excavation, the lateral earth pressure outside the pit is not a fixed value along the depth and length of the pit; its magnitude is determined by the deformation of the retaining structure. Therefore, a uniform stress release coefficient cannot be used to assess the magnitude of unloading on the entire foundation pit sidewall; the magnitude of the unloading induced by foundation pit excavation needs to be calculated in conjunction with the lateral deformation of the retaining structure. Summary of the Invention

[0004] To address the shortcomings of the existing technology, this invention provides a calculation method for the deformation of adjacent tunnels induced by foundation pit excavation, taking into account spatial effects.

[0005] This invention is achieved using the following technical solution:

[0006] A calculation method for deformation of adjacent tunnels induced by foundation pit excavation considering spatial effects includes the following steps:

[0007] (1) Determine the three-dimensional curve of the lateral deformation of the retaining wall;

[0008] (2) Determine the soil unloading caused by the deformation of the retaining wall induced by the excavation of the foundation pit;

[0009] (3) The deformation control equations of the adjacent tunnel were determined using the Winkler foundation and Timoshenko beam models;

[0010] (4) Determine the parameters to solve the deformation of the adjacent tunnel.

[0011] In the above technical solution, further, in step (1), a certain point on the retaining wall of the foundation pit is targeted. The formula for calculating its three-dimensional deformation is as follows:

[0012]

[0013]

[0014]

[0015] In the formula, y0 is the coordinate along the length of the excavation pit, z0 is the coordinate along the depth of the excavation pit, and f max H represents the maximum deformation of the retaining wall closest to the tunnel side. max f max The location is defined by the following depths: H represents the excavation depth of the foundation pit, and D represents the insertion depth of the retaining wall. This is the length of the foundation pit.

[0016] Furthermore, step (2) specifically includes:

[0017] Establish the relationship between lateral earth pressure unloading and displacement:

[0018]

[0019]

[0020]

[0021] In the formula, p m p is the maximum unloadable soil mass outside the pit, p0 is the at-rest earth pressure, p a For active earth pressure, p u For unloading induced by soil displacement, k u The unloading coefficient related to soil displacement, where S is the soil displacement, S acr This represents the ultimate displacement of the active soil mass.

[0022] At the location of the retaining wall, the deformation of the retaining wall is equal to the soil displacement. Therefore, the soil unloading caused by the deformation of the retaining wall induced by the excavation of the foundation pit is:

[0023]

[0024]

[0025] It is Poisson's ratio.

[0026] Furthermore, step (3) specifically includes:

[0027] The tunnel is simplified as a Timoshenko beam placed on the Winkler foundation, which is subjected to soil unloading. At that time, the differential equilibrium equation for the deformation of the adjacent tunnel is:

[0028]

[0029] In the formula, E t I t For the equivalent bending stiffness of the tunnel, (κGA) eq Let w(y) be the equivalent shear stiffness of the tunnel, w(y) be the horizontal deformation of the tunnel, k be the foundation reaction coefficient, and D be the equivalent shear stiffness of the tunnel. t The diameter of the tunnel;

[0030] Using the finite difference method, the tunnel is divided into n equal parts, each with a length of l, and has a total of n+1 nodes; then the finite difference form of the above equation is transformed into:

[0031] In the formula For the horizontal deformation of the i-th tunnel node, The load on the i-th tunnel node

[0032] Assume the boundary conditions are that the tunnel ends are free, i.e., shear force. and Bending moment and All are 0:

[0033]

[0034] Each node i has a deformation control equation. If we write the n+1 deformation control equations as a system of equations and then rewrite them in matrix form, the matrix expression is:

[0035]

[0036] In the formula: K1 is the tunnel stiffness matrix, K2 is the foundation shear stiffness matrix, and K3 is the foundation stiffness matrix. P1 is the column vector of horizontal deformation of the tunnel; P2 is the column vector of additional load caused by the excavation of the foundation pit; P3 is the column vector of load correction; P4 is the supplementary vector for solution.

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] Furthermore, in step (4):

[0047] Equivalent bending stiffness of tunnel E t I t for:

[0048]

[0049]

[0050] In the formula, E is the neutral axis position. c Let A be the elastic modulus of the tunnel segment. c Let n be the cross-sectional area of ​​the tunnel segment. t k represents the number of bolts. b k is the average linear stiffness of the joint bolts. b =E b A b / l b E b Let A be the elastic modulus of the bolt. b l is the cross-sectional area of ​​the bolt. b l is the bolt length. s For the ring width;

[0051] Tunnel equivalent shear stiffness (κGA) eq for:

[0052]

[0053] In the formula, ζ is the correction coefficient, and κ is the correction coefficient. b κ c These are the shear coefficients for bolts and segments, respectively, G b and G c These are the shear stiffness of the bolts and the segments, respectively.

[0054] The foundation reaction coefficient k is:

[0055]

[0056] In the formula, E s This is the elastic modulus of the soil.

[0057] The beneficial effects of this invention are as follows:

[0058] This invention considers the impact of the spatial deformation of the retaining wall on the unloading of the soil outside the pit, thus overcoming the shortcomings of the original analysis method, which uses a constant unloading coefficient and does not consider the variation of the unloading coefficient with the depth and length of the retaining wall. Furthermore, it employs an analysis model that considers tunnel shear deformation, making the calculation model closer to the actual situation. Attached Figure Description

[0059] Figure 1 A schematic diagram of the foundation pit excavation and unloading, and the adjacent tunnel;

[0060] Figure 2 This is a curve comparing the method of the present invention with measured data. Detailed Implementation

[0061] like Figure 1 This is a schematic diagram of the foundation pit excavation and unloading, and the adjacent tunnel.

[0062] This invention provides a calculation method for deformation of adjacent tunnels induced by foundation pit excavation, considering spatial effects. The specific steps are as follows:

[0063] 1) Determine the spatial distribution of lateral deformation of the retaining wall.

[0064] Targeting a specific point on the retaining wall of the foundation pit The formula for calculating its three-dimensional deformation is as follows:

[0065]

[0066]

[0067]

[0068] In the formula, y0 is the coordinate along the length of the excavation pit, z0 is the coordinate along the depth of the excavation pit, and f max H represents the maximum deformation of the retaining wall closest to the tunnel side. max f maxThe location is defined by the following depths: H represents the excavation depth of the foundation pit, and D represents the insertion depth of the retaining wall. f is the length of the foundation pit. max and H max The design calculations or measured values ​​of the support structure can be used for analysis depending on the different stages of the project.

[0069] 2) Determine the soil unloading caused by the deformation of the retaining wall induced by the excavation of the foundation pit;

[0070] Establish the relationship between lateral earth pressure unloading and displacement:

[0071]

[0072]

[0073]

[0074] In the formula, p m p is the maximum unloadable soil mass outside the pit, p0 is the at-rest earth pressure, p a For active earth pressure, p u For unloading induced by soil displacement, k u The unloading coefficient related to soil displacement, where S is the soil displacement, S acr This represents the ultimate displacement of the active soil mass.

[0075] Calculate soil unloading induced by the deformation of the retaining structure

[0076] At the location of the retaining wall, the deformation of the retaining wall is equal to the displacement of the soil. Therefore, the calculation formula for the soil unloading induced by the deformation of the retaining structure is as follows:

[0077] According to Mindlin's solution, the deformation of the retaining wall induces unloading of the soil at (x, y, z) outside the pit. The expression is:

[0078]

[0079]

[0080] It is Poisson's ratio.

[0081] 3) The deformation control equations of the adjacent tunnel were determined using the Winkler foundation and Timoshenko beam models.

[0082] The tunnel is simplified as a Timoshenko beam placed on the Winkler foundation, which is subjected to soil unloading. At that time, the differential equilibrium equation for the deformation of the adjacent tunnel is:

[0083]

[0084] In the formula, E t I t For the equivalent bending stiffness of the tunnel, (κGA) eq Let w(y) be the equivalent shear stiffness of the tunnel, w(y) be the horizontal deformation of the tunnel, k be the foundation reaction coefficient, and D be the equivalent shear stiffness of the tunnel. t The diameter of the tunnel, due to In the diagram, x and z represent the distance from the tunnel axis to the foundation pit and the burial depth, respectively. These can be determined in advance and can therefore be simplified as follows: .

[0085] Using the finite difference method, the tunnel is divided into n equal parts, each of length l, with a total of n+1 nodes. The finite difference form of the above equation then transforms into:

[0086] In the formula, For the horizontal deformation of the i-th tunnel node, Let be the load on the i-th tunnel node.

[0087] The boundary condition is that the tunnel ends are free, i.e., shear force. and Bending moment and All are 0:

[0088]

[0089] Each node i has a deformation control equation. If we write the n+1 deformation control equations as a system of equations and then rewrite them in matrix form, the matrix expression is:

[0090]

[0091] In the formula: K1 is the tunnel stiffness matrix, K2 is the foundation shear stiffness matrix, and K3 is the foundation stiffness matrix. P1 is the column vector of horizontal deformation of the tunnel; P2 is the column vector of additional load caused by the excavation of the foundation pit; P3 is the column vector of load correction; P4 is the supplementary vector for solution.

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] 4) Determine the parameters to solve for the deformation of adjacent tunnels.

[0102] 4.1 Equivalent Bending Stiffness of Tunnels

[0103]

[0104]

[0105] In the formula, E is the neutral axis position. c Let A be the elastic modulus of the tunnel segment. c Let n be the cross-sectional area of ​​the tunnel segment. t k represents the number of bolts. b k is the average linear stiffness of the joint bolts. b =E b A b / l b E b Let A be the elastic modulus of the bolt. b l is the cross-sectional area of ​​the bolt. b l is the bolt length. s The width of the ring.

[0106] 5.2 Equivalent Shear Stiffness of the Tunnel

[0107]

[0108] In the formula, ζ is the correction coefficient, and κ is the correction coefficient. b κ c These are the shear coefficients for bolts and segments, respectively, G b and G c These are the shear stiffness of the bolts and the segments, respectively.

[0109] 5.3 Foundation reaction coefficient

[0110] The expression for the foundation reaction coefficient is:

[0111]

[0112] In the formula, E s This is the elastic modulus of the soil.

[0113] Example

[0114] The foundation pit is 70 m long (L), with an excavation depth (H) and a retaining wall insertion depth (D) of 10 m and 12 m respectively. The distance (d) from the adjacent tunnel to the edge of the foundation pit is 10.3 m, the tunnel axis burial depth (h) is 10.1 m, and the longitudinal equivalent bending stiffness (E) is... t I t 1.8×10 5 MN·m 2 Maximum deformation of the retaining wall f max Take 16 mm, its location is H max The foundation soil elastic modulus E is 10 m. s Taking a compression modulus of 12.4 MPa (twice) and a Poisson's ratio of 0.35, the ultimate displacement S of the soil is... acr 0.4%H

[17] .

[0115] As can be seen from the comparison between the calculation method of the present invention and the measured data, the calculation method of the present invention and the measured data have achieved good consistency in terms of deformation trend. Overall, the calculation method of the present invention has a certain degree of reliability and applicability.

Claims

1. A calculation method for deformation of adjacent tunnels induced by foundation pit excavation considering spatial effects, characterized in that, Includes the following steps: (1) Determine the three-dimensional curve of the lateral deformation of the retaining wall; (2) Determine the soil unloading caused by the deformation of the retaining wall induced by the excavation of the foundation pit; (3) The deformation control equations of the adjacent tunnel were determined using the Winkler foundation and Timoshenko beam models; (4) Determine the parameters to solve for the deformation of adjacent tunnels; The specific steps (2) are as follows: Establish the relationship between lateral earth pressure unloading and displacement: ， ， ， In the formula, p m p is the maximum unloadable soil mass outside the pit, p0 is the at-rest earth pressure, p a For active earth pressure, p u For unloading induced by soil displacement, k u The unloading coefficient related to soil displacement, where S is the soil displacement, S acr This represents the ultimate displacement of the active soil mass. At the location of the retaining wall, the deformation of the retaining wall is equal to the soil displacement. Therefore, the soil unloading caused by the deformation of the retaining wall induced by the excavation of the foundation pit is: ， ， Where is Poisson's ratio, H is the excavation depth of the foundation pit, and D is the insertion depth of the retaining wall. The length of the foundation pit. Let y0 be the lateral deformation of the retaining wall at coordinates (0, y0, z0), where y0 is the coordinate along the length of the pit and z0 is the coordinate along the depth of the pit.

2. The calculation method for deformation of adjacent tunnels induced by foundation pit excavation considering spatial effects, as described in claim 1, is characterized in that... In step (1), a certain point on the retaining wall of the foundation pit is considered. The formula for calculating its three-dimensional deformation is as follows: ， ， ， In the formula, y0 is the coordinate along the length of the excavation pit, z0 is the coordinate along the depth of the excavation pit, and f max H represents the maximum deformation of the retaining wall closest to the tunnel side. max f max The location is defined by the following depths: H represents the excavation depth of the foundation pit, and D represents the insertion depth of the retaining wall. This is the length of the foundation pit.

3. The calculation method for deformation of adjacent tunnels induced by foundation pit excavation considering spatial effects, as described in claim 1, is characterized in that... The specific steps (3) are as follows: The tunnel is simplified as a Timoshenko beam placed on the Winkler foundation, which is subjected to soil unloading. At that time, the differential equilibrium equation for the deformation of the adjacent tunnel is: ， In the formula, E t I t For the equivalent bending stiffness of the tunnel, (κGA) eq Let w(y) be the equivalent shear stiffness of the tunnel, w(y) be the horizontal deformation of the tunnel, k be the foundation reaction coefficient, and D be the equivalent shear stiffness of the tunnel. t The diameter of the tunnel; Using the finite difference method, the tunnel is divided into n equal parts, each with a length of l, and has a total of n+1 nodes; then the finite difference form of the above equation is transformed into: In the formula For the horizontal deformation of the i-th tunnel node, Let be the load on the i-th tunnel node; Assume the boundary conditions are that the tunnel ends are free, i.e., shear force. and Bending moment and All are 0: ， Each node i has a deformation control equation. If we write the n+1 deformation control equations as a system of equations and then rewrite them in matrix form, the matrix expression is: ， In the formula: K1 is the tunnel stiffness matrix, K2 is the foundation shear stiffness matrix, and K3 is the foundation stiffness matrix. P1 is the column vector of horizontal deformation of the tunnel; P2 is the column vector of additional load caused by the excavation of the foundation pit; P3 is the column vector of load correction; P4 is the supplementary vector for solution. ， ， ， ， ， ， ， ， 。 4. The calculation method for deformation of adjacent tunnels induced by foundation pit excavation considering spatial effects, as described in claim 3, is characterized in that... In step (4) mentioned above: Equivalent bending stiffness of tunnel E t I t for: ， ， In the formula, E is the neutral axis position. c Let A be the elastic modulus of the tunnel segment. c Let n be the cross-sectional area of ​​the tunnel segment. t k represents the number of bolts. b k is the average linear stiffness of the joint bolts. b =E b A b / l b E b Let A be the elastic modulus of the bolt. b l is the cross-sectional area of ​​the bolt. b l is the bolt length. s For the ring width; Tunnel equivalent shear stiffness (κGA) eq for: ， In the formula, ζ is the correction coefficient, and κ is the correction coefficient. b κ c These are the shear coefficients for bolts and segments, respectively, G b and G c These are the shear stiffness of the bolts and the segments, respectively. The foundation reaction coefficient k is: ， In the formula, E s This is the elastic modulus of the soil.

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