Accurate prediction method for adjacent tunnel upheaval deformation caused by foundation pit excavation and capable of considering soil friction influence

Abstract

The invention discloses a method for accurately predicting upheaval deformation of adjacent tunnels caused by foundation pit excavation by considering the influence of soil friction, which comprises the following steps of: firstly, determining size parameters of a foundation pit and an existing tunnel and physical and mechanical parameters of the tunnel and a soil body, and determining a stress mode of the tunnel and a model sketch of interaction of the foundation pit and the tunnel; determining the additional stress of the tunnel; then establishing a total energy formula of a tunnel upheaval deformation system of a Pasternak foundation model considering soil friction, 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, based on the Pasternak foundation model, the influence of axial soil body friction of the tunnel on tunnel deformation is considered, so that the calculated data better conform to the measured value. The method is simple and practical in matrix analysis, and has guiding significance for predicting the upheaval deformation of the adjacent tunnel caused by excavation of the foundation pit.

Description

Technical Field

[0001] This invention relates to the field of underground engineering technology, and in particular to an accurate prediction method for the uplift deformation of adjacent tunnels caused by foundation pit excavation that can take into account the effects of soil friction. Background Technology

[0002] With the development of society and economy and the expansion of urban underground space, the number of subway construction projects in cities has surged. Many construction projects are located adjacent to subway tunnels. Taking foundation pit engineering as an example, as the foundation pit is gradually excavated, it disturbs the soil below, further altering the stress and strain field around the adjacent tunnel. How to evaluate the impact of foundation pit excavation on adjacent tunnels has become a research hotspot in the field of underground engineering.

[0003] The excavation of a foundation pit can have the following harmful effects on adjacent tunnels. Firstly, significant tunnel deformation itself poses a considerable risk. Large deformations generate substantial bending moments, leading to frequent cracking, increased leakage, and even mudslides, which can severely damage the tunnel in the long run. Secondly, the excavation causes soil unloading, and the creep of the unloaded soil also affects tunnel deformation. Therefore, accurately predicting the uplift displacement and bending moment of adjacent tunnels caused by foundation pit excavation is crucial.

[0004] Existing research on the vertical deformation of adjacent tunnels caused by foundation pit excavation simplifies the tunnel as an Euler-Bernoulli beam resting on Winkler and Pasternak foundation models, establishing tunnel mechanical equilibrium control equations based on the stress state. However, this approach neglects the system energy changes during tunnel deformation, and the influence of tunnel axial soil friction on tunnel deformation energy has not been reported. The existence of friction can effectively limit the stress and deformation of existing tunnels, making the prediction of tunnel-soil interaction more accurate. The Pasternak foundation model used in this invention overcomes the inability of the Winkler foundation to consider the influence of soil shear deformation, and the method of this invention is simple and practical in matrix analysis. Summary of the Invention

[0005] The purpose of this invention is to address the problems existing in the prior art by providing an accurate prediction method for the uplift deformation of adjacent tunnels caused by foundation pit excavation that takes into account the influence of soil friction. This method provides a simple and practical way to make more accurate predictions of the uplift deformation of adjacent tunnels caused by foundation pit excavation.

[0006] The objective of this invention is achieved through the following technical solution: a precise prediction method for the vertical deformation of adjacent tunnels caused by foundation pit excavation, taking into account the influence of soil friction, the method 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 the soil;

[0008] (2) Determine the stress mode of the tunnel including the axial soil friction of the tunnel and the simplified diagram of the interaction model between the foundation pit and the tunnel;

[0009] (3) Determine the magnitude of the additional stress on the tunnel, assume that the axial soil friction of the tunnel is a uniform load acting on the tunnel, obtain the axial soil friction force of the tunnel based on the weight of the soil on the shield and the interface friction angle between the shield and the soil, and establish the total energy formula of the tunnel deformation system of the Pasternak foundation model considering the influence of soil friction.

[0010] (4) The analytical matrix of tunnel uplift deformation w is obtained based on the energy variational principle;

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

[0012] Furthermore, in step (1), the dimensional parameters include the tunnel diameter, burial depth, pit length, width and depth, shortest distance from the midpoint of the pit to the tunnel, tunnel bending stiffness and the angle between the long side of the pit and the tunnel axis; the physical and mechanical parameters include the soil elastic modulus and Poisson's ratio.

[0013] Furthermore, in step (2), the existing tunnel is simplified into an Euler-Bernoulli beam placed on the Pasternak foundation model, and the influence of the axial soil friction force of the tunnel in the Pasternak foundation model is introduced to determine the simplified model diagram.

[0014] Furthermore, in step (3), the axial soil friction force of the tunnel is calculated as follows:

[0015] f = τ = σtanδ

[0016] Where τ is the shear stress between the shield and the nearby soil; σ is the weight of the soil at any point on the shield; and δ is the interface friction angle between the shield and the nearby soil, which is approximately 35° in soft soil areas.

[0017] Furthermore, the total energy of tunnel deformation T is the sum of bending deformation energy T1, work done by the foundation reaction force in the Pasternak model T2, work done by the additional load T3, and work done by the axial soil friction force in the tunnel T4, that is:

[0018] T = T1 + T2 + T3 + T4.

[0019] Furthermore, the work T4 done by the axial soil friction force in the tunnel is as follows:

[0020]

[0021] In the formula, D is the tunnel diameter; f is the axial soil friction force of the tunnel; w is the tunnel uplift deformation; and L1 is half the tunnel length. Furthermore, based on the energy variational method, we know that:

[0022] δT=δT1+δT2+δT3+δT4=0

[0023] In the formula, δ represents the variational symbol; at this point, we can obtain:

[0024] (K1+K2-K3+K4)·A=q

[0025] In the formula: 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 axial soil friction stiffness matrix; q is the additional stress vector.

[0026] Furthermore, the axial soil friction stiffness matrix of the tunnel is as follows:

[0027]

[0028] Where D is the tunnel diameter; f is the axial soil friction force of the tunnel; and L1 is half the tunnel length.

[0029] Furthermore, by setting the calculation parameter G to 0, the Pasternak foundation model on which the tunnel rests can be degenerated into a Winker foundation model. The simplified model diagram shows the tunnel placed on a Pasternak foundation model that considers soil shear deformation, overcoming the limitation of the Winker foundation model in not considering soil shear deformation. The magnitude of the additional stress generated by the excavation of the foundation pit on the tunnel at different angles is achieved by changing the angle between the pit and the tunnel axis. Compared to traditional mechanical equilibrium theory, the method of this invention obtains the analytical matrix of the tunnel heave deformation w based on the energy variational principle.

[0030] The beneficial effects of this invention are as follows: It employs an accurate prediction method for the uplift deformation of adjacent tunnels caused by foundation pit excavation, which considers the influence of soil friction, overcoming the problem that the Winkler foundation model cannot consider soil shear deformation. Furthermore, this invention obtains the analytical matrix w of tunnel uplift deformation based on the energy variational principle, overcoming the limitations of traditional theories that study the interaction between tunnels and soil from the perspective of mechanical equilibrium. This invention considers the influence of axial soil friction on tunnel deformation, enabling the frictional force to effectively limit tunnel deformation during the prediction of tunnel-soil interaction. This makes the data calculated by this invention more consistent with measured values, and the resulting analytical method is simpler and easier to understand, possessing significant value for widespread application. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a schematic diagram illustrating an accurate prediction method for the uplift deformation of adjacent tunnels caused by foundation pit excavation, taking into account the effects of soil friction.

[0033] Figure 2 This is a schematic diagram illustrating the interaction between the foundation pit and the existing tunnel according to the present invention.

[0034] Figure 3 This is a top view showing the relative positions of the foundation pit and the tunnel in this invention.

[0035] Figure 4 This is a force diagram of the tunnel unit along the tunnel axis according to the present invention.

[0036] Figure 5 This is a diagram of the tunnel-soil interaction model under the Pasternak foundation of the present invention.

[0037] Figure 6 A comparison chart of the calculation results provided in this implementation case and the on-site monitoring data.

[0038] 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 Implementation

[0039] To facilitate understanding of the present invention, the invention will be further described below with reference to the accompanying drawings and engineering examples.

[0040] according to Figure 1 As shown, this invention provides an accurate prediction method for the uplift deformation of adjacent tunnels caused by foundation pit excavation, which can take into account the influence of soil friction. The specific steps are described below:

[0041] S1: Determine the dimensional parameters of the foundation pit and the existing tunnel, as well as the physical and mechanical parameters of the tunnel and the soil: The tunnel is an infinitely long beam, and the two ends of the tunnel are simplified to be free at both ends, ignoring the impact of the foundation pit excavation on the two ends of the tunnel.

[0042] The foundation pit has an excavation depth of 5m, a width of 46m, and a length of 110m; the tunnel has an outer diameter of 5.5m, an angle of 90° between the edge of the foundation pit and the tunnel, and a burial depth of 10.9m.

[0043] The soil weight is 16.9 kN / m. 3The soil modulus is taken as 30.8 MPa, and the longitudinal friction force of the tunnel is 247 kN / m. 2 The tunnel's bending stiffness is 6.74 × 10⁻⁶. 5 MN·m 2 .

[0044] S2: The existing tunnel is simplified into an Euler-Bernoulli beam placed on the Pasternak foundation model. The influence of the axial soil friction force of the tunnel in the Pasternak foundation model is introduced to determine the stress mode of the tunnel and a simplified diagram of the interaction model between the pit and the tunnel.

[0045] According to the specifications, the allowable value w for the maximum heave deformation displacement of the tunnel is determined. max The maximum tunnel uplift displacement occurs at the point closest to the center of the tunnel and the excavation pit. The tunnel uplift deformation pattern is a process in which the displacement gradually decreases towards both ends of the tunnel from the point of maximum displacement until the displacement at both ends of the tunnel approaches zero. The displacement deformation diagram is shown below. Figure 2 As shown in the top view, the relative positions of the excavation pit and the tunnel are as follows: Figure 3 As shown.

[0046] S3: The additional stress applied to the underlying tunnel by the excavation of the foundation pit is obtained by using the Mindlin formula. The magnitude of the additional stress generated at the tunnel axis by the excavation of the foundation pit at different angles is changed by changing the angle between the tunnel and the side length of the foundation pit. Based on the determined magnitude of the additional stress on the tunnel, the stress-strain equation of the vertical displacement w of the tunnel is established for the Pasternak foundation model that can take into account the influence of soil friction.

[0047] S31: As Figure 2 As shown, the expression for the magnitude of the additional stress at the tunnel axis caused by the excavation of the foundation pit is as follows:

[0048]

[0049] in, p = γH, where γ is the soil mass, 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 burial depth of the tunnel axis, λ and η are the coordinates of a point at the bottom of the foundation pit in the λOη coordinate system, and d represents the differential sign.

[0050] S32: Considering that the tunnel axis is not parallel to the pit wall, the coordinate system on the tunnel axis needs to be incorporated into the global coordinate system of the pit. The relationship between the two coordinate planes is as follows:

[0051]

[0052] In the formula, S0 is the shortest distance from the center point of the foundation pit to the tunnel axis;

[0053] The axial soil friction in the tunnel can be further assumed to be a uniform load acting on the tunnel (e.g., Figure 4 As shown), and satisfies:

[0054] f = τ = σtanδ

[0055] Where τ is the shear stress between the shield and the nearby soil; σ is the weight of the soil at any point on the shield; and δ is the interface friction angle between the shield and the nearby soil, which is approximately 35° in soft soil areas.

[0056] The aforementioned tunnel uplift deformation displacement w satisfies:

[0057]

[0058] In the formula: 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 represented as:

[0059]

[0060] The diagram of the Pasternak foundation tunnel-soil interaction model is shown below. Figure 5 As shown, considering that the total energy of tunnel deformation T can be divided into the sum of bending deformation energy T1, the work done by the foundation reaction force T2 and the work done by the additional load T3 in the Pasternak model, and the work done by the soil friction force along the tunnel axis T4, that is...

[0061]

[0062] In the formula, EI is the tunnel bending stiffness; D is the tunnel diameter; q is the additional stress on the tunnel; k is the foundation elastic stiffness; G is the foundation shear layer stiffness; f is the tunnel axial soil friction force; k and G can be calculated using the following method:

[0063]

[0064] In the formula, E s v and z0 are the soil modulus and Poisson's ratio, respectively; z0 is the tunnel axis burial depth; h is the soil shear layer thickness; and h = 2.5D.

[0065] S4: The analytical matrix of tunnel uplift deformation w is obtained based on the energy variational principle. Based on the energy variational method, it can be seen that:

[0066] δT=δT1+δT2+δT3+δT4=0

[0067] In the formula, δ represents the variational symbol;

[0068] Right now

[0069]

[0070] At this point, we can obtain

[0071] (K1+K2-K3+K4)·A=q

[0072] In the formula: K1 is the tunnel bending stiffness matrix, K2 is the soil elastic stiffness matrix, K3 is the soil shear stiffness matrix, and K4 is the tunnel axial soil friction stiffness matrix; q is the additional stress vector; the expressions for K1, K2, K3, and K4 are as follows:

[0073]

[0074] S5: The bending moment and shear force of the tunnel are obtained based on the Euler-Bernoulli beam theory; the expressions for the tunnel bending moment and shear force are as follows:

[0075]

[0076] The method described in this embodiment was used to calculate the subway project on a plaza foundation pit. The calculation results were compared with the on-site monitoring data. Figure 6 As shown, from Figure 6 It can be seen that the calculation results of this implementation case are close to the trend of the field monitoring data, and the peak values ​​are basically consistent. This proves that the calculation method of this implementation case can be used for the settlement calculation and prediction analysis of the underlying tunnel caused by the excavation of adjacent foundation pits in soft soil areas. Moreover, the calculation method is relatively simple and practical, and it is of great significance for estimating the impact of foundation pit excavation on adjacent tunnels.

[0077] The above embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A precise prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation, taking into account the effects of soil friction, characterized in that, The method includes 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 the soil; (2) Determine the stress mode of the tunnel including the axial soil friction of the tunnel and the simplified diagram of the interaction model between the foundation pit and the tunnel; (3) Determine the magnitude of the additional stress on the tunnel, assume that the axial soil friction of the tunnel is a uniform load acting on the tunnel, obtain the axial soil friction force of the tunnel based on the weight of the soil on the shield and the interface friction angle between the shield and the soil, and establish the total energy formula of the tunnel deformation system of the Pasternak foundation model considering the influence of soil friction. (4) The analytical matrix of tunnel uplift deformation w is obtained based on the energy variational principle; (5) Based on the Euler-Bernoulli beam theory, the expressions for the tunnel's rotation angle, bending moment, and shear force are obtained, and the tunnel's uplift deformation displacement is solved.

2. The accurate prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation, considering the influence of soil friction, as described in claim 1, is characterized in that... In step (1), the dimensional parameters include tunnel diameter, burial depth, pit length, width and depth, shortest distance from the midpoint of the pit to the tunnel, tunnel bending stiffness and the angle between the long side of the pit and the tunnel axis; the physical and mechanical parameters include soil elastic modulus and Poisson's ratio.

3. The accurate prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation, considering the influence of soil friction, as described in claim 1, is characterized in that... In step (2), the existing tunnel is simplified into an Euler-Bernoulli beam placed on the Pasternak foundation model. The influence of the axial soil friction force of the tunnel in the Pasternak foundation model is introduced to determine the simplified model diagram.

4. The accurate prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation, considering the influence of soil friction, as described in claim 1, is characterized in that... In step (3), the axial soil friction force of the tunnel is calculated as follows: f = τ = σtanδ; Where τ is the shear stress between the shield and the nearby soil; σ is the weight of the soil at any point on the shield; and δ is the interface friction angle between the shield and the nearby soil, which is approximately 35° in soft soil areas.

5. The accurate prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation, considering the influence of soil friction, as described in claim 1, is characterized in that... The total energy of tunnel deformation, T, is the sum of bending deformation energy T1, work done by the foundation reaction force in the Pasternak model T2, work done by the additional load T3, and work done by the axial soil friction force in the tunnel, T4. T = T1 + T2 + T3 + T4.

6. The accurate prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation, considering the influence of soil friction, as described in claim 5, is characterized in that... The work T4 done by the axial soil friction force in the tunnel is as follows: In the formula, D is the tunnel diameter; f is the axial soil friction force of the tunnel, w is the tunnel uplift deformation, and L1 is half the tunnel length.

7. The accurate prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation, considering the influence of soil friction, as described in claim 5, is characterized in that... Based on the energy variational method, we know that: δT=δT1+δT2+δT3+δT4=0; In the formula, δ represents the variational symbol; at this point, we can obtain: (K1+K2-K3+K4)·A=q; In the formula: 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 axial soil friction stiffness matrix; q is the additional stress vector.

8. The accurate prediction method for vertical deformation of adjacent tunnels caused by foundation pit excavation, considering the influence of soil friction, as described in claim 7, is characterized in that... The tunnel axial soil friction stiffness matrix is ​​as follows: Where D is the tunnel diameter; f is the axial soil friction force of the tunnel; and L1 is half the tunnel length.

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