Accurate prediction method for vertical deformation of adjacent tunnel caused by foundation pit excavation under consideration of lateral soil body effect

Abstract

The invention discloses an accurate prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil mass, which comprises the following steps: firstly, determining size parameters of a foundation pit and an existing tunnel and physical and mechanical parameters of the tunnel and the soil mass, determining a stress mode of the tunnel and a model sketch of interaction between the foundation pit and the tunnel, and determining additional stress of the tunnel; then establishing a total energy formula of a tunnel upheaval deformation system of a Pasternak foundation model considering the influence of a lateral soil body and axial internal force of the tunnel, and obtaining a tunnel upheaval deformation w matrix analysis based on an energy variation principle; and finally, according to an Euler-Bernoulli beam theory, a bending moment expression and a shearing force expression of the tunnel are obtained. According to the method, the influence of the lateral soil body and the axial internal force of the tunnel on tunnel deformation is considered on the basis of the Pasternak foundation model, so that the data obtained through calculation more conforms to the measured value, matrix analysis is simple and practical, and the method has guiding significance on prediction of vertical deformation of the adjacent tunnel caused by foundation pit excavation.

Description

Technical Field

[0001] The present invention relates to the field of underground engineering technology, and in particular to a precise prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil. Background Art

[0002] With socioeconomic development and the expansion of urban underground space, the number of subway construction projects underway has surged. Many of these projects are located adjacent to subway tunnels. For example, excavation of foundation pits disturbs the underlying soil, further altering the stress and strain fields surrounding adjacent tunnels. Evaluating the impact of foundation pit excavation on adjacent tunnels has become a research hotspot in underground engineering.

[0003] Excavation can have several detrimental effects on adjacent tunnels. First, significant tunnel deformation poses significant risks to the tunnel itself. This large deformation generates significant bending moments, leading to frequent cracking, increased leakage, and even mud seepage. This long-term damage is extremely detrimental to the tunnel. Furthermore, excavation unloads the soil, and the creep of this unloaded soil also impacts tunnel deformation. Therefore, accurately predicting the vertical displacement and bending moments of adjacent tunnels caused by excavation is crucial.

[0004] Existing techniques for studying the vertical deformation of adjacent tunnels caused by foundation pit excavation simplify the tunnel into an Euler-Bernoulli beam placed on a Winkler foundation model, establishing tunnel mechanical equilibrium control equations based on the stress state. However, these techniques ignore the system energy changes during the tunnel deformation process, and the effects of the tunnel's lateral soil and axial internal forces on the tunnel's deformation energy have not been reported. The Pasternak foundation model adopted in the present invention overcomes the Winkler foundation's inability to consider the effects of soil shear deformation, and the matrix analysis method of the present invention is simple and practical. Summary of the Invention

[0005] The purpose of the present invention is to provide an accurate prediction method for the vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil, in order to address the problems existing in the prior art, and to make a more accurate prediction of the vertical deformation of adjacent tunnels caused by foundation pit excavation through a simple and practical method.

[0006] The object of the present invention is achieved through the following technical solution: a method for accurately predicting the vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil, comprising the following steps:

[0007] (1) Determine the dimensional parameters of the foundation pit and the existing tunnel as well as the physical and mechanical parameters of the tunnel and soil;

[0008] (2) Determine the tunnel's stress pattern and a schematic diagram of the interaction model between the foundation pit and the tunnel;

[0009] (3) Determine the magnitude of the additional stress on the tunnel and establish the stress-strain equation for the tunnel's vertical displacement w;

[0010] (4) Obtain the tunnel displacement w matrix analytically based on the difference method and boundary conditions;

[0011] (5) Based on the Euler-Bernoulli beam theory, the expressions of the tunnel's rotation angle, bending moment, and shear force are obtained, and the tunnel's uplift deformation displacement is obtained by solving them.

[0012] Furthermore, the expression of the additional stress magnitude of the tunnel is as follows:

[0013]

[0014] in, p＝γH ,γ is the soil weight, B and L are the length and width of the foundation pit, H is the depth of the foundation pit, υ is the Poisson's ratio of the soil, z0 is the buried depth of the tunnel axis, and are the coordinates of a point on the bottom of the foundation pit in the λOη coordinate system, and d represents the differential sign.

[0015] Furthermore, considering that the tunnel axis and the foundation pit wall are not parallel, the coordinate system on the tunnel axis needs to be incorporated into the global coordinate system of the foundation pit. The relationship between the two coordinate planes is as follows:

[0016]

[0017] Where S0 is the shortest distance from the center of the foundation pit to the tunnel axis;

[0018] The tunnel uplift deformation displacement w satisfies:

[0019]

[0020] Where: w represents the tunnel uplift deformation; L1 is half the tunnel length; A i is an undetermined coefficient; x is the coordinate value along the longitudinal direction of the tunnel; i = 0, 1, 2, ..., n-1, n; n represents that the tunnel is divided into n micro units, and the matrix can be expressed as:

[0021]

[0022] Furthermore, considering that the total deformation energy T of the tunnel can be divided into the sum of the bending deformation energy T1, the work of the foundation reaction force T2 and the additional load work T3 in the Pasternak model, the work done by the lateral soil of the tunnel T4, and the work done by the axial internal force of the tunnel T5, that is,

[0023] Where EI is the tunnel bending stiffness; D is the tunnel diameter; q is the additional stress on the tunnel; k is the elastic stiffness of the foundation, G is the stiffness of the foundation shear layer; N is the axial internal force of the tunnel. k and G can be calculated using the following method:

[0024]

[0025]

[0026] Where, E s is the soil modulus; υ is the Poisson's ratio of the soil; z0 is the depth of the tunnel axis; h is the thickness of the soil shear layer; and h = 2.5D

[0027] Based on the energy variation method, we know that:

[0028] δT=δT1+δT2+δT3+δT4+δT5=0

[0029] Where represents the symbol of variation;

[0030] Right now

[0031]

[0032] At this time,

[0033] (K1+K2-K3+K4+K5)·A=q

[0034] Where: K1 is the tunnel bending stiffness matrix, K2 is the soil elastic stiffness matrix, K3 is the soil shear stiffness matrix, K4 is the tunnel lateral soil stiffness matrix; K5 is the tunnel axial internal force stiffness matrix; q is the additional stress vector; the expressions of K1, K2, K3, K4 and K5 are:

[0035]

[0036]

[0037] The tunnel bending moment and shear force expressions are:

[0038]

[0039] Furthermore, the specific implementation steps are as follows:

[0040] S1: Determine the cross-sectional parameters of the foundation pit and the existing tunnel, including the tunnel diameter, burial depth, length, width and depth of the foundation pit, and the shortest distance from the midpoint of the foundation pit to the tunnel; the tunnel stiffness is the tunnel bending stiffness; the angle is the angle between the long side of the foundation pit and the tunnel axis; the soil physical and mechanical parameters include the soil elastic modulus Es and Poisson's ratio υ;

[0041] S2: Simplify the existing tunnel into an Euler-Bernoulli beam placed on the Pasternak foundation model;

[0042] S3: Use the Mindlin formula to obtain the additional stress exerted by the foundation pit excavation on the underlying tunnel, and establish the total energy formula of the tunnel uplift deformation system based on the Pasternak foundation model;

[0043] S4: Obtain the tunnel uplift deformation w matrix analytically based on the energy variation principle;

[0044] S5: Obtain the bending moment and shear force of the tunnel based on Euler-Bernoulli beam theory.

[0045] Furthermore, in step (2), the influence of the lateral soil and tunnel axial internal force of the Pasternak foundation model is introduced to determine the model diagram.

[0046] Furthermore, the tunnel is placed on a Pasternak foundation model containing two parameters to reflect the tunnel-soil interaction process.

[0047] Furthermore, the additional stress generated by excavation of foundation pits at different angles on the tunnel axis can be changed by changing the angle between the tunnel and the foundation pit side lengths.

[0048] Furthermore, the tunnel is an infinitely long beam, and the two ends of the tunnel are simplified to be free, and the impact of foundation pit excavation on the two ends of the tunnel is ignored.

[0049] Furthermore, the calculation parameter G is set to 0, and the foundation model on which the tunnel is placed, the Pasternak foundation model, is degenerated into the Winker foundation model.

[0050] The model diagram places the tunnel on a Pasternak foundation model that can take into account soil shear deformation, overcoming the problem that the Winkler foundation model cannot take into account soil shear deformation.

[0051] The precise calculation method is to change the angle between the foundation pit and the tunnel axis to realize the additional stress generated by the foundation pit excavation on the tunnel at different angles; compared with the traditional mechanical equilibrium theory, this method obtains the tunnel uplift deformation w matrix analysis based on the energy variation principle.

[0052] The beneficial effects of the present invention are that, by adopting the accurate method provided by the present invention for predicting the uplift deformation of the underlying tunnel caused by foundation pit excavation, the problem that the Winkler foundation model cannot take into account the shear deformation of the soil is overcome; and the present invention obtains the tunnel uplift deformation w matrix analysis based on the energy variation principle, which overcomes the traditional theory that studies the interaction between the tunnel and the soil from the perspective of mechanical equilibrium; the present invention considers the influence of the lateral soil and axial internal force of the tunnel on the tunnel deformation, so that the data calculated by the present invention is more consistent with the measured value, and the calculated analysis is simpler and easier to understand, and has good promotion and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0054] Figure 1 Schematic diagram of a method for accurately predicting the vertical deformation of adjacent tunnels caused by lower foundation pit excavation, taking into account lateral soil and axial internal forces.

[0055] Figure 2 It is a schematic diagram of the interaction between the foundation pit and the existing tunnel of the present invention.

[0056] Figure 3 It is a top view of the relative positions of the foundation pit and the tunnel of the present invention.

[0057] Figure 4 This is the force diagram of the tunnel unit body of the present invention.

[0058] Figure 5 This is a diagram of the tunnel-soil interaction model under the Pasternak foundation of the present invention.

[0059] Figure 6 A comparison chart of the calculation results provided by this implementation case and the on-site monitoring data.

[0060] In the figure: 1 is the tunnel; 2 is the foundation pit; 3 is the ground; 4 is the additional load q(x); 5 is the soil shear stiffness G; 6 is the soil elastic stiffness k. DETAILED DESCRIPTION

[0061] In order to facilitate understanding of the present invention, the present invention is further described below with reference to the accompanying drawings and engineering examples.

[0062] according to Figure 1 As shown, the present invention provides an accurate prediction method for the vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil. The specific steps are described as follows:

[0063] S1: Determine the dimensional parameters of the foundation pit and existing tunnel as well as the physical and mechanical parameters of the tunnel and soil:

[0064] The excavation depth of the foundation pit is 5m, the width of the foundation pit is 46m, and the length is 110m; the outer diameter of the tunnel is 5.5m, the angle between the edge of the foundation pit and the tunnel is 90°, and the tunnel is buried at a depth of 10.9m.

[0065] The soil modulus is 16.8 MPa, and the tunnel bending stiffness is 6.74×10 5 MN·m 2 , the axial internal force of the tunnel is 20MN.

[0066] S2: Determine the tunnel's stress pattern and a simplified diagram of the interaction model between the foundation pit and the tunnel;

[0067] Determine the maximum allowable vertical deformation value w of the tunnel according to the specification max The maximum vertical displacement of the tunnel occurs at the closest distance between the tunnel and the foundation pit center; the vertical deformation mode of the tunnel is a process of gradually decreasing from the maximum displacement to the two ends of the tunnel until the displacement at both ends of the tunnel is close to 0. The displacement deformation diagram is shown in Figure 2 As shown, the relative position of the foundation pit and the tunnel is shown in the top view. Figure 3 shown.

[0068] S3: Determine the magnitude of the additional stress on the tunnel and establish a stress-strain equation related to the vertical displacement w of the tunnel;

[0069] S31: Figure 4 As shown, the additional stress of the tunnel is calculated as follows:

[0070]

[0071] in, p＝γH ,γ is the soil weight, H is the excavation depth of the foundation pit, L and B are the length and width of the foundation pit, v is the Poisson's ratio of the soil, z0 is the buried depth of the tunnel axis and are the coordinates of a point on the bottom of the foundation pit in the λOη coordinate system, and d represents the differential sign.

[0072] S32: Considering that the tunnel axis and the pit wall are not parallel, the coordinate system on the tunnel axis needs to be incorporated into the global coordinate system of the foundation pit. The relationship between the two coordinate planes is as follows:

[0073]

[0074] Where S0 is the shortest distance from the center of the foundation pit to the tunnel axis.

[0075] The tunnel uplift deformation displacement w satisfies:

[0076]

[0077] Where: w represents the tunnel uplift deformation; L1 is half the tunnel length; A i is an undetermined coefficient; x is the coordinate value along the longitudinal direction of the tunnel; i = 0, 1, 2, ..., n-1, n; n represents that the tunnel is divided into n micro units, and the matrix can be expressed as:

[0078]

[0079] The tunnel-soil interaction model under the Pasternak foundation is shown in the figure Figure 5 As shown in Figure 2, considering that the total deformation energy T of the tunnel can be divided into the bending deformation energy T1, the sum of the foundation reaction work T2 and the additional load work T3 in the Pasternak model, the lateral soil work T4 of the tunnel, and the axial internal force work T5 of the tunnel, that is,

[0080]

[0081] Where EI is the tunnel bending stiffness; D is the tunnel diameter; q is the additional stress on the tunnel; k is the elastic stiffness of the foundation, and G is the shear layer stiffness of the foundation. k and G can be calculated using the following method:

[0082]

[0083] Where, E s is the soil modulus; υ is the Poisson's ratio of the soil; z0 is the depth of the tunnel axis; h is the thickness of the soil shear layer; and h = 2.5D;

[0084] Based on the energy variation method, we know that:

[0085] δT=δT1+δT2+δT3+δT4+δ5=0

[0086] where represents the symbol of variation.

[0087] Right now

[0088]

[0089] At this time,

[0090] (K1+K2-K3+K4+K5)·A=q

[0091] Where: K1 is the tunnel bending stiffness matrix, K2 is the soil elastic stiffness matrix, K3 is the soil shear stiffness matrix, K4 is the tunnel lateral soil stiffness matrix; K5 is the tunnel axial internal force stiffness matrix; q is the additional stress vector; the expressions of K1, K2, K3, K4 and K5 are:

[0092]

[0093] The tunnel bending moment and shear force expressions are:

[0094]

[0095] The calculation method of this embodiment is used to calculate the subway project on a square foundation pit. The calculation results are compared with the on-site monitoring data. Figure 6 As shown, from Figure 6 As can be seen, the calculation results of this implementation case closely follow the trends of the on-site monitoring data, and the peak values ​​are essentially identical. This demonstrates that the calculation method used in this implementation case can be used to calculate and predict the settlement of the underlying tunnel caused by adjacent foundation pit excavation in soft soil areas. The method is relatively simple and practical, and is of great significance for estimating the impact of foundation pit excavation on adjacent tunnels.

[0096] The above embodiments are used to illustrate the present invention rather than to limit the present invention. Any modifications and changes made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for accurately predicting the vertical deformation of adjacent tunnels caused by foundation pit excavation under the influence of lateral soil, comprising the following steps: (1) Determine the dimensional parameters of the foundation pit and the existing tunnel as well as the physical and mechanical parameters of the tunnel and soil; (2) Determine the tunnel's stress pattern and a simplified diagram of the interaction model between the foundation pit and the tunnel; the stress pattern includes bending deformation, foundation reaction in the Pasternak model, additional load, lateral work done by the tunnel soil, and axial work done by the tunnel internal force; (3) Determine the magnitude of the additional stress on the tunnel and establish the stress-strain equation for the tunnel's vertical displacement w; (4) Obtain the tunnel displacement w matrix analytically based on the difference method and boundary conditions; (5) Based on the Euler-Bernoulli beam theory, the expressions of the tunnel's rotation angle, bending moment, and shear force are obtained, and the tunnel's uplift deformation displacement is obtained by solving them.

2. The accurate method for predicting the uplift deformation of the underlying tunnel caused by foundation pit excavation according to claim 1 is characterized in that: The expression of the additional stress of the tunnel is as follows: in, p＝γH ,γ is the soil weight, B and L are the length and width of the foundation pit, H is the depth of the foundation pit, v is the Poisson's ratio of the soil, z0 is the buried depth of the tunnel axis, and are the coordinates of a point on the bottom of the foundation pit in the λOη coordinate system, and d represents the differential sign.

3. The accurate method for predicting the uplift deformation of the underlying tunnel caused by foundation pit excavation according to claim 1 is characterized in that: Considering that the tunnel axis and the foundation pit wall are not parallel, the coordinate system on the tunnel axis needs to be incorporated into the global coordinate system of the foundation pit. The relationship between the two coordinate planes is as follows: Where S0 is the shortest distance from the center of the foundation pit to the tunnel axis, and α is the angle between the long side of the foundation pit and the tunnel axis; The tunnel uplift deformation displacement w satisfies: Where: w represents the tunnel uplift deformation; L1 is half the tunnel length; A i is the coefficient to be determined; x is the coordinate value along the longitudinal direction of the tunnel; i = 0, 1, 2, ..., n-1, n; n means that the tunnel is divided into n micro units, and the matrix can be expressed as:

4. The accurate method for predicting the uplift deformation of the underlying tunnel caused by foundation pit excavation according to claim 1 is characterized in that: Considering that the total deformation energy T of the tunnel can be divided into the bending deformation energy T1, the sum of the foundation reaction work T2 and the additional load work T3 in the Pasternak model, the lateral soil work T4 of the tunnel, and the axial internal force work T5 of the tunnel, that is, Where EI is the tunnel bending stiffness; D is the tunnel diameter; q is the additional stress on the tunnel; k is the elastic stiffness of the foundation, G is the stiffness of the foundation shear layer; N is the axial internal force of the tunnel. k and G can be calculated using the following method: Where, E s is the soil modulus; υ is the Poisson's ratio of the soil; z0 is the depth of the tunnel axis; h is the thickness of the soil shear layer; and h = 2.5D Based on the energy variation method, we know that: δT=δT1+δT2+δT3+δT4+δT5=0 Where represents the symbol of variation; Right now At this time, (K1+K2-K3+K4+K5)·A=q Where: K1 is the tunnel bending stiffness matrix, K2 is the soil elastic stiffness matrix, K3 is the soil shear stiffness matrix, K4 is the tunnel lateral soil stiffness matrix; K5 is the tunnel axial internal force stiffness matrix; q is the additional stress vector; the expressions of K1, K2, K3, K4 and K5 are: The tunnel bending moment and shear force expressions are:

5. The accurate method for predicting the uplift deformation of the underlying tunnel caused by foundation pit excavation according to claim 1 is characterized in that: The specific implementation steps are as follows: S1: Determine the cross-sectional parameters of the foundation pit and the existing tunnel, including the tunnel diameter, burial depth, length, width and depth of the foundation pit, and the shortest distance from the midpoint of the foundation pit to the tunnel; the tunnel stiffness is the tunnel bending stiffness; the angle is the angle between the long side of the foundation pit and the tunnel axis; the soil physical and mechanical parameters include the soil elastic modulus Es and Poisson's ratio υ; S2: Simplify the existing tunnel into an Euler-Bernoulli beam placed on the Pasternak foundation model; S3: Use the Mindlin formula to obtain the additional stress exerted by the foundation pit excavation on the underlying tunnel, and establish the total energy formula of the tunnel uplift deformation system based on the Pasternak foundation model; S4: Obtain the tunnel uplift deformation w matrix analytically based on the energy variation principle; S5: Obtain the bending moment and shear force of the tunnel based on Euler-Bernoulli beam theory.

6. The method for accurately predicting vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil as claimed in claim 5, characterized in that: In step (2), the influence of lateral soil and axial internal force of the Pasternak foundation model is introduced to determine the model diagram.

7. The method for accurately predicting vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil as claimed in claim 5, characterized in that: The tunnel is placed on a Pasternak foundation model containing two parameters to reflect the tunnel-soil interaction process.

8. The method for accurately predicting vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil as claimed in claim 5, characterized in that: By changing the angle between the tunnel and the foundation pit side length, the additional stress generated by the foundation pit excavation at different angles on the tunnel axis can be changed.

9. The method for accurately predicting vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil as claimed in claim 5, characterized in that: The tunnel is an infinitely long beam, and the two ends of the tunnel are simplified to be free, and the impact of foundation pit excavation on the two ends of the tunnel is ignored.

10. The method for accurately predicting vertical deformation of adjacent tunnels caused by foundation pit excavation under the action of lateral soil as claimed in claim 25, characterized in that: The calculation parameter G is set to 0, and the foundation model on which the tunnel is placed is degenerated from the Pasternak foundation model to the Winker foundation model.

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