Rectangular pipe-jacking tunnel excavation stratum deformation analysis method
By establishing a three-dimensional elastic layered body model and discrete boundary element method, combined with the interpolation form of higher order isoparameter unit, the error problem of the deformation calculation of the top tube tunnel excavation formation in the lamellar formation in the existing technology is solved, and the calculation results with higher accuracy are achieved, verifying the reliability of the method.
Patent Information
- Application Number
- CN202510314670.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-18
- Publication Date
- 2025-06-27
AI Technical Summary
It is difficult for the prior art to accurately calculate the stratigraphic deformation caused by excavation of top pipe tunnels in stratigraphic formations, especially due to the complex interlayer relationship of the formations. Simple equivalent substitution will lead to large errors in the calculation results and actual conditions.
A three-dimensional elastic layered body model is proposed. By establishing a matrix partial differential equation of state vectors with respect to geometric coordinates, and converting it into matrix normal differential equations through Fourier integral transformation, the matrix normal differential equation is solved to obtain the transfer relationship between different spatial state vectors, and combining discrete boundary element method and higher-order isoparameter unit interpolation form, the basic solutions of stress and displacement in the layered formation are calculated.
This method can more accurately consider the layered characteristics of the formation and the non-uniform convergence of the soil in the boundary of the top tube tunnel, improving the calculation accuracy. The reliability of the proposed theoretical calculation method is verified by comparison with engineering monitoring data and other theoretical calculation results.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of formation deformation analysis, and specifically to a method for analyzing the formation deformation caused by the excavation of a rectangular pipe-jacking tunnel. Background Art
[0002] During the construction of a pipe-jacking tunnel, the overlying formation and the formation traversed are usually layered formations formed by the deposition and stacking of different formations. Due to the different soil properties, soil layer thicknesses, and soil parameters of each formation, it is extremely difficult to solve the deformation of the soil inside the formation. Controlling the formation deformation and settlement is the key core of the safe construction of underground projects. Excessive formation deformation will cause major accidents such as formation collapse or uplift, collapse of adjacent buildings, and damage to underground pipelines. Therefore, it is of great significance to solve the formation deformation caused by the excavation of a pipe-jacking tunnel in a layered formation.
[0003] The calculation methods for the ground settlement caused by the construction disturbance of a pipe-jacking tunnel mainly include empirical methods, analytical (semi-analytical) methods, numerical simulation methods, laboratory test methods, and artificial intelligence prediction methods, etc. According to investigations, a large number of theoretical studies have been carried out on the analytical (semi-analytical) method, but most of them are aimed at homogeneous formations, and there is less research on layered formations such as soft upper and hard lower, hard and soft alternating, and sand-clay interbedded formations. Some scholars use equivalent parameters to regard the layered formation as a homogeneous formation for derivation and calculation. However, due to the extremely complex interlayer interaction relationship of the formation, simple equivalent substitution will cause a large error between the calculation result and the actual situation, lacking rationality and reliability.
[0004] The existing calculation methods have the following disadvantages: (1) The assumptions of the existing theoretical calculation methods for the model and the excavation convergence mode around the tunnel hole are too idealized and do not conform to the engineering reality; (2) Most of the existing theoretical methods are aimed at homogeneous formations and cannot calculate the formation deformation caused by the excavation of a pipe-jacking tunnel under the conditions of heterogeneous formations such as soft upper and hard lower, hard and soft alternating, and sand-clay interbedded formations; (3) Some solutions use equivalent parameters to regard the layered formation as a homogeneous formation for derivation and calculation. However, due to the extremely complex interlayer interaction relationship of the formation, simple equivalent substitution will cause a large error between the calculation result and the actual situation, lacking rationality and reliability; The theoretical calculation method for the formation deformation caused by the excavation of a pipe-jacking tunnel in a layered formation proposed by the present invention can rely on the construction parameters and hydrogeological parameters of the pipe-jacking tunnel to solve the formation deformation caused by the excavation of a pipe-jacking tunnel in a layered formation, providing theoretical support for the safe construction of the pipe-jacking tunnel. Summary of the Invention
[0005] The purpose of the present invention is: aiming at the problem that it is difficult to directly solve the formation displacement and stress caused by the pipe-jacking construction in a layered formation, the present invention proposes a theoretical calculation method for solving the formation deformation and settlement caused by the excavation of a pipe-jacking tunnel in a layered formation.
[0006] To achieve the above object, the present invention provides the following technical solution: A method for analyzing the deformation of the excavation stratum of a rectangular pipe jacking tunnel, comprising the following steps: Step 1: According to the distribution characteristics of the layered stratum and the construction process of the pipe jacking tunnel, establish a three-dimensional elastic layer model and put forward reasonable and feasible basic assumptions; Step 2: Determine the construction parameters of the pipe jacking tunnel project and the soil parameters of the layered stratum; the construction parameters include: the excavation size of the cutter head of the pipe jacking machine and the size of the pipe segment; the soil parameters include: soil unit weight, cohesion, internal friction angle, elastic modulus, Poisson's ratio and stratum thickness; Step 3: Taking the i th layer as an example, establish a matrix partial differential equation (1) of the state vector with respect to the geometric coordinates, and convert the matrix partial differential equation into a matrix ordinary differential equation (3) through Fourier integral transformation (2). In formula (3), C is solved through formula (4); Solve the matrix ordinary differential equation (3) to obtain the transfer relationship (5) between different spatial state vectors where Q is the spatial transfer matrix; To eliminate the calculation overflow or ill-conditioned matrix phenomenon caused by the positive exponential term, derive the stiffness matrix (6) of the single-layer elastic layer through the transfer matrix, and form the overall stiffness matrix (12) of the elastic layer according to the traditional finite element method. K in the overall stiffness matrix (12) i is obtained from formula (7); K1, K2, K2, K2 in formula (7) are obtained from formula (8), formula (9), formula (10) and formula (11) respectively; In order to solve the fundamental solutions of stress and displacement in the layered stratum and facilitate the subsequent analysis and calculation of tunnel boundary stress and stratum settlement deformation, apply a load at any position in the model, the position where the load acts is , and the horizontal plane where this point is located is used as the interface between the m th layer and the m +1th layer; obtain the overall stiffness matrix (13) under the action of the concentrated load, and combine the boundary conditions of the layered soil stratum and the source point concentrated load to solve the surface spatial state vector ; due to the existence of the concentrated load, the calculation formulas of the spatial state vectors at different depths are different. When the spatial state vector to be obtained is above the concentrated load, substitute it into formula (14), and when the spatial state vector to be obtained is below the concentrated load, substitute it into formula (15). Combine the obtained results and use Fourier integral transformation (2) to obtain the fundamental solutions of stress and displacement at any field point in the layered soil stratum under the action of the concentrated load; ; ; ; ; Among them, E i is the elastic modulus of the i th layer of soil; μ i is the Poisson's ratio of the i th layer of soil; h i is the distance from the bottom of the i th layer of soil to the ground surface; K i is the stiffness matrix of the i th layer of soil; K 1n is the overall stiffness matrix of the soil layers from the first layer to the n th layer; Step 4: Based on the construction parameters of the pipe-jacking tunnel, establish the boundary equation (16) for the excavation of the tunnel perimeter. According to the modified tunnel boundary and the number of discrete elements N, calculate the non-uniform convergence mode of each node on the boundary, determine the displacements of each node on the tunnel boundary (17), and convert the formula (17) into the high-order isoparametric element interpolation form (18): Combine the displacement-controlled discrete boundary element method to solve the stress boundary conditions of the shield tunnel perimeter using the formulas (20), (21), (22), (23), and (24). In this step, the stress and displacement boundary conditions of the tunnel perimeter have been solved; Among them, the relationship between formulas (11) and (12) is formula (13); In formula (16): a is the long side of the excavation contour, b is the short side of the excavation contour, r is the chamfer radius of the excavation contour, a c is the long side after correcting the over-excavation amount, b c is the short side after correcting the over-excavation amount, r c is the chamfer radius after correcting the over-excavation amount; In formula (17): u i is the displacement of the i point on the tunnel boundary along the x direction, v i is the displacement of the i point on the tunnel boundary along the y direction,w i The displacement of the point on the tunnel boundary i along the z direction; Equation (19) is the fixed formula for high-order isoparametric elements, N ( ξ ) and ξ will not be explained; Write the boundary element method equation of the tunnel boundary S in matrix form and discretize it to obtain: Substitute (19) into (20) to obtain: where, is the boundary stress of the j th k node on the arbitrary element m along the is the boundary displacement of the j th k node on the arbitrary element m along the At the source point i acting on the coordinate m in the j direction, the boundary response load of the k th n node on the element At the source point i acting on the coordinate m in the j direction, the boundary response displacement of the k th n node on the element and are the boundary influence coefficients of the source point i on the j th k node of the element is the boundary response load of the i th m node on the element j in the k direction when the boundary unit load acts on the coordinate n in the is the boundary response displacement of the i th mWhen applying a boundary unit load in a certain direction, for the element j on k the node at n the boundary response displacement in a certain direction; Step 5: Take each node on the boundary of the pipe-jacking tunnel as the source point in turn, substitute its boundary stress and displacement as the concentrated load and displacement in the formation into the overall stiffness matrix to calculate the deformation settlement of the layered formation w iz , and use numerical integration (25) to perform iterative summation calculations on the nodes on the entire tunnel boundary to obtain the deformation settlement at the depth z of the layered formation under the non-uniform convergence condition as: Among them, N is the number of discrete elements on the tunnel boundary; S is the perimeter of the tunnel boundary.
[0007] Compared with the prior art, the beneficial effects of the present invention are: 1. The equivalent method of layered formation and the uniform convergence mode in the prior art are too idealized. The present invention proposes a theoretical calculation method for solving the deformation settlement of the formation excavated by a pipe-jacking tunnel in a layered formation aiming at the problem that it is difficult to directly solve the formation displacement and stress caused by the pipe-jacking construction in a layered formation. This method is based on the geological exploration parameters and construction parameters of the pipe-jacking tunnel, considering the layered distribution characteristics of the formation, the non-uniform convergence around the pipe-jacking tunnel and the small deformation disturbance of the formation during the pipe-jacking tunnel construction, and establishes a three-dimensional elastic layer model. The present invention can fully consider the layered characteristics of the formation and the non-uniform convergence of the soil body at the boundary of the pipe-jacking tunnel. By using the discrete boundary element method and introducing high-order isoparametric elements, the calculation accuracy is improved, and the reliability of the proposed theoretical calculation method is verified by comparing with the engineering monitoring data and other theoretical calculation results.
[0008] To theoretically solve the deformation settlement of the layered formation, it is first necessary to clarify the overall stiffness matrix and the initial boundary conditions of the elastic layer. The initial boundary conditions include the ground surface, the deep formation and the tunnel perimeter. Among them, the initial boundary conditions of the ground surface and the deep formation are known conditions, and the deformation settlement inside the formation is solved based on the overall stiffness matrix and the discrete boundary element method.
[0009] 2. The present invention establishes a three-dimensional elastic layer model aiming at the layered characteristics of the formation and the excavation method of the pipe-jacking tunnel; based on the non-uniform convergence mode of the soil body at the boundary of the pipe-jacking tunnel, combines the discrete boundary element method to solve the stress boundary conditions of the pipe-jacking tunnel perimeter; takes each node on the boundary of the pipe-jacking tunnel as the source point in turn, and uses its boundary stress and displacement as the concentrated load and displacement in the formation to calculate the deformation settlement at any depth inside the layered formation at this point w iz, the deformation settlement at any depth inside the stratified formation under non-uniform convergence conditions is calculated by numerically integrating and iteratively summing the nodes on the entire tunnel boundary. w z 。 BRIEF DESCRIPTION OF THE DRAWINGS
[0010] Figure 1 FIG. 1 is a schematic flow chart of the idea of a theoretical calculation method for the excavation stratum deformation of a pipe jacking tunnel in a stratified formation provided by an embodiment of the present invention.
[0011] Figure 2 Three-dimensional elastic layer model.
[0012] Figure 3 For non-uniform convergence mode.
[0013] Figure 4 FIG. 2 is a layout diagram of monitoring measurement points.
[0014] Figure 5 FIG. 3 is a geological cross-section of Example 1.
[0015] Figure 6 FIG. 4 is a comparison diagram of surface settlements in Example 1.
[0016] Figure 7 FIG. 5 is a geological cross-section of Example 2.
[0017] Figure 8 FIG. 6 is a comparison diagram of surface settlements in Example 2. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.
[0019] In the embodiments of the present invention, the solution idea is as shown in FIG. 1. Considering the layered distribution characteristics of the formation, a three-dimensional elastic layer model as shown in FIG. 2 is established, and the following assumptions are proposed: Figure 1 As shown in FIG. 2, and the following assumptions are proposed: Figure 2 (1) The model consists of several homogeneous and isotropic semi-space elastic layer bodies, and their plastic deformation is not considered; (1) The model is composed of several homogeneous and isotropic semi-space elastic layer bodies, and its plastic deformation is not considered; (2) The surface of the model is unconstrained and there is no surface load; (3) The stress and displacement are completely continuous at the interface between layers.
[0020] According to as shown in FIG. 2 Figure 3For the non-uniform convergence mode of the tunnel periphery shown, calculate the boundary displacement conditions of the tunnel periphery, and solve the formation deformation caused by the excavation of the rectangular pipe jacking tunnel in the layered formation according to the foregoing steps.
[0021] Table 1 shows the setting of the layered formation parameters for a certain pipe jacking tunnel project. According to the formation layering situation, a typical monitoring section is selected for case verification. The measuring points on the monitoring section of this project follow the principle of being denser near and sparser far away, and the measuring point spacings are 3.5 m, 5 m, 8 m, and 10 m in sequence. 8 measuring points are arranged on each monitoring section, and the measuring point layout is as Figure 4 shown.
[0022] Table 1 Formation Parameter Setting
[0023] Example 1: According to the detailed exploration report of the formation given in the project, the overburden thickness of the pipe jacking underground passage is 11.5 m. The overlying formation from top to bottom is: 2.4 m of miscellaneous fill and 9.1 m of medium-coarse sand. Monitoring section 1 is set in the front of the passage. The overlying formation of this section is 2.4 m of miscellaneous fill and 9.1 m of medium-coarse sand, and the two formations are distributed in layers, as Figure 5 shown.
[0024] It can be Figure 6 seen that the monitoring data at monitoring point 1 of the project has the same change trend as the theoretical calculation result. The surface settlement curve follows a normal distribution, is symmetric about the tunnel axis left and right, and the maximum surface settlement is located directly above the tunnel axis. As the distance from the axis increases, the surface settlement gradually decreases to zero. At the measuring point on the left side of the pipe jacking tunnel, the engineering monitoring data is 10.11 mm, the result obtained by the Peck formula is 12.68 mm, and the error reaches 2.57 mm. The theoretical calculation result of the present invention is 10.72 mm, and the error is only 0.61 mm. In addition, at the 10 m monitoring point, the Peck curve has approached 0, but the engineering monitoring data is 2.58 mm, and the theoretical calculation result of the present invention is 2.41 mm. It can be clearly seen that the theoretical method proposed by the present invention is more consistent with the engineering practice.
[0025] Example 2: Example 2 is located at the tail of the passage. The overlying formation of this section is 2.1 m of miscellaneous fill, 4.3 m of medium-coarse sand, 1.2 m of silty clay, and 3.9 m of medium-coarse sand. The four formations are distributed in layers, and the cross-section geological conditions are as Figure 7 shown.
[0026] Figure 8It is a comparison chart of the monitoring data at monitoring section 2 and the theoretical calculation results. It can be seen from the chart that the monitoring data and the theoretical calculation results have the same change trend, and the surface settlement curve obeys the normal distribution. Through comparison, it can be known that at the measuring point of 3.5m, the engineering monitoring value is 9.24mm, the result obtained by the Peck formula is 13.21mm, and the error from the engineering monitoring data is 3.97mm, reaching 42.96%; while the theoretical calculation result of this paper is 10.07mm, and the error from the engineering monitoring data is only 0.83mm. It can be clearly seen that the theoretical method proposed in this paper is more in line with the engineering practice. The accuracy and superiority of the proposed theoretical calculation method are verified through the above case.
[0027] The above is only the preferred specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution of the present invention and its inventive concept, makes equivalent replacements or changes, and should be covered by the protection scope of the present invention.
Claims
1. A method for analyzing ground deformation during rectangular pipe-jacking tunnel excavation, characterized in that: The steps include: Step 1: According to the distribution characteristics of the layered strata and the construction process of the pipe-jacking tunnel, a three-dimensional elastic layered body model is established, and reasonable and feasible basic assumptions are proposed; Step 2: Determine the construction parameters of the pipe jacking tunnel project and the soil parameters of the layered strata; The construction parameters include: the excavation size of the pipe jacking machine cutter head and the size of the pipe section; the soil parameters include: soil weight, cohesion, internal friction angle, elastic modulus, Poisson's ratio and stratum thickness; Step 3: Take the i Taking the layer as an example, the matrix partial differential equation (1) of the state vector with respect to the geometric coordinates is established, and the matrix partial differential equation is transformed into the matrix ordinary differential equation (3) through the Fourier integral transformation (2). In formula (3), [ C ] Solved by formula (4); Solving the matrix ordinary differential equation (3) yields the state vectors of different spaces The transitive relationship between them is (5), where [ Q ] is the spatial transfer matrix; In order to eliminate the calculation overflow or ill-conditioned matrix phenomenon caused by the positive exponential term, the stiffness matrix (6) of the single-layer elastic layer is derived by the transfer matrix, and the overall stiffness matrix (12) of the elastic layer is formed according to the traditional finite element method. The K in the overall stiffness matrix (12) is i It is obtained by formula (7); K1, K2, K2, K2 in formula (7) are obtained by formula (8), formula (9), formula (10) and formula (11) respectively; In order to solve the basic solution of stress and displacement in the layered strata and facilitate the subsequent analysis and calculation of tunnel boundary stress and stratum settlement deformation, loads are applied at any position in the model. The load acting position is , the horizontal plane where this point is located is taken as the m Layer and m +1 interlayer interface; obtain the overall stiffness matrix (13) under the concentrated load, and solve the surface space state vector by combining the boundary conditions of the stratified soil layer and the source point concentrated load ; Due to the existence of concentrated loads, the calculation formulas for the spatial state vector at different depths are different. When the required spatial state vector is above the concentrated load, it is substituted into formula (14); when the required spatial state vector is below the concentrated load, it is substituted into formula (15). The required results are combined with Fourier integral transformation (2) to obtain the basic solution of stress and displacement at any field point in the stratified soil layer under the action of concentrated loads; ； ； ； ； in, E i For the i Elastic modulus of the soil layer; μ i For the i Poisson's ratio of the soil layer; h i For the i The distance from the bottom of the soil layer to the ground surface; K i ] is the first i Stiffness matrix of layer soil; K ] 1n For the first to the n The global stiffness matrix of the soil layer; Step 4: Based on the construction parameters of the pipe jacking tunnel, the boundary equation of the tunnel excavation is established (16). According to the corrected tunnel boundary and the number of discrete units N, the non-uniform convergence mode of each node on the boundary is calculated, and the displacement of each node on the tunnel boundary is determined (17). Formula (17) is converted into a high-order isoparametric unit interpolation form (18): Combined with the displacement-controlled discrete boundary element method, formulas (20), (21), (22), (23) and (24) are used to solve the stress boundary conditions around the shield tunnel. In this step, the stress and displacement boundary conditions around the tunnel have been solved; The relationship between formula (11) and (12) is formula (13); In formula (16): a is the long side of the excavation profile, b is the short side of the excavation profile, r is the chamfer radius of the excavation profile, a c To correct the long side after over-excavation, b c To correct the short side after over-excavation, r c It is the chamfer radius after correcting the over-excavation; In formula (17): u i On the tunnel boundary i Point Edge x Direction displacement, v i On the tunnel boundary i Point Edge y Direction displacement, w i On the tunnel boundary i Point Edge z Directional displacement; Formula (19) is a fixed formula for high-order isoparametric units. N ( ξ ) and ξ No explanation is given; The boundary element method equation of the tunnel boundary S is written in matrix form and discretized to obtain: Substituting (19) into (20), we obtain: in, For any unit j Previous k Node along m Boundary stress in the direction; For any unit j Previous k Node along m Boundary displacement in direction; At the source i Action coordinates m When the boundary unit load is in the direction of j superior k Node in n Boundary response loads in the direction; At the source i Action coordinates m When the boundary unit load is in the direction of j superior k Node in n Boundary response displacement in the direction; and Source i For Unit j Previous k The boundary influence coefficient of each node; At the source i Action coordinates m When the boundary unit load is in the direction of j superior k Node in n Boundary response loads in the direction; At the source i Action coordinates m When the boundary unit load is in the direction of j superior k Node in n Boundary response displacement in the direction; Step 5: Take each node on the boundary of the jacking tunnel as the source point in turn, and substitute its boundary stress and displacement as the concentrated load and displacement in the stratum into the overall stiffness matrix to calculate the deformation and settlement of the stratified soil strata. w iz , the depth of the layered strata under the non-uniform convergence condition can be obtained by iteratively summing up the nodes on the entire tunnel boundary using numerical integration (25). z The deformation and settlement at is: in, N is the number of discrete tunnel boundary units; S is the tunnel boundary perimeter.