A method for predicting ground deformation caused by construction gaps in steep-slope tunnels

Abstract

This invention discloses a method for predicting ground deformation caused by construction gaps in steep-slope tunnels. The prediction method includes the following steps: a tunnel boring machine excavates the tunnel along a steep-slope construction path; based on the three-dimensional source-sink method theory, the vertical deformation of the soil caused by unit volume voids within a semi-infinite body is obtained; a three-dimensional spatial model of the steep-slope tunnel is established, and combined with the construction path of the steep-slope tunnel, the actual construction gaps at the tunnel face are obtained; the unit volume voids are integrated within the volume domain formed by the tunnel face along the construction path of the steep-slope tunnel to obtain the ground settlement caused by the actual construction gaps at the tunnel face. The advantages of this invention are: based on the three-dimensional source-sink method, it fully considers the actual construction characteristics of steep-slope tunnels, can accurately predict ground deformation, and provides a research foundation for future calculation methods on ground deformation caused by asymmetric ground loss at the horizon.

Description

Technical Field

[0001] This invention relates to the technical field of tunnel engineering, and in particular to a method for predicting ground deformation caused by construction gaps in steep-slope tunnels. Background Technology

[0002] Shield tunneling or TBM construction has the advantage of minimal impact on ground deformation, especially in controlling vertical soil displacement. While numerous predictive devices and methods exist for vertical soil displacement caused by ground losses, most of these projects involve straight tunnels in a horizontal plane, with few methods available to predict ground deformation caused by construction gaps in steeply graded tunnels. For shield tunneling or TBM excavation along steep slopes, the tunnel axis elevation is constantly changing, making conventional predictive equipment inapplicable. Furthermore, the actual grouting process is extremely complex; the actual grouting rate cannot reach 100%, and it is affected by factors such as compaction, ground conditions, transportation, and over-excavation, resulting in grouting losses. Therefore, the effects of structural gravity and grouting filling effects must be comprehensively considered. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting ground deformation caused by construction gaps in steep-slope tunnels, based on the shortcomings of the prior art. By combining the construction technology of the tunnel boring machine during the tunneling process along the construction path of the steep-slope tunnel, the ground settlement caused by ground loss in three-dimensional space can be accurately calculated, thereby accurately predicting the ground settlement caused by ground loss.

[0004] The objective of this invention is achieved through the following technical solutions:

[0005] A method for predicting ground deformation caused by construction gaps in steep tunnels, characterized in that the prediction method includes the following steps:

[0006] (S1) The tunnel boring machine excavates the tunnel along a steep slope. Based on the three-dimensional source-sink method theory, the vertical deformation s of the soil within a semi-infinite body due to the void volume per unit volume is obtained. z ;

[0007] (S2) Establish a three-dimensional spatial model of the steep slope tunnel, and combine it with the construction path of the steep slope tunnel to obtain the actual construction gap G at the tunnel face. e ;

[0008] (S3) Integrate the unit volume void within the volume domain formed by the tunnel face along the construction path of the steep-slope tunnel to obtain the actual construction gap G at the tunnel face. e The resulting ground subsidence S z .

[0009] Step S1 includes the following steps:

[0010] Establish a three-dimensional rectangular coordinate system, in which the origin O, the x-axis, and the y-axis are all located on the ground surface, and the z-axis is vertically downward;

[0011] The soil mass is a semi-infinite body bounded by the Earth's surface, encompassing only its lower portion. Assuming the soil mass is an unbounded infinite body, the vertical deformation component at point P(x,y,z) caused by a unit volume void at point F(x0,y0,z0) within this infinite body is:

[0012]

[0013] In the formula: R1=[(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] 1 / 2 ;

[0014] Let there be a point F′(x0,y0,–z0) at the mirror position of point F(x0,y0,–z0). The vertical deformation component at point P(x,y,z) caused by the unit volume void at point F′(x0,y0,–z0) is:

[0015]

[0016] In the formula: R2=[(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 1 / 2 ;

[0017] Applying the shear stress generated by the unit volume void at the Earth's surface in the opposite direction to the surface, the vertical deformation component generated at point P(x,y,z) is calculated as follows:

[0018]

[0019] In the formula: μ is the Poisson's ratio of the soil; u and t are both independent variables of the function; c and b are the upper and lower limits of integration; R3 = [(xu)] 2 +(yt) 2 +z 2 ] 1 / 2 ;

[0020] The vertical deformation s of the soil within the semi-infinite body due to the void volume per unit volume z for:

[0021]

[0022] Step S2 includes the following steps:

[0023] A three-dimensional spatial model of a tunnel with a steep gradient of γ is established, where downward excavation by the tunnel boring machine is the positive direction and upward excavation is the negative direction.

[0024] The burial depth of the center O′ of the working face is h, and the burial depth h(x0) at point (x0, y0, z0) is:

[0025] h(x0) = h + x0tanγ;

[0026] The actual construction gap G at the working face e Including the tail gap V s and grouting filling V g They are respectively:

[0027] V s =π(R) 2 -r 2 ),

[0028] V g =πλ(1-α1-α2-α3-α4)(R 2 -r 2 ),

[0029] In the formula: R and r are the outer diameters of the tunnel boring machine and the lining, respectively; λ is the grouting rate; α1 is the compaction loss coefficient; α2 is the soil loss coefficient; α3 is the conveying loss coefficient; α4 is the over-excavation loss coefficient;

[0030] Due to the gravity of the lining and grout, the outer edge of the lining and the bottom of the grout will be close to the inner edge of the shield. The actual construction gap G at the working face... e for:

[0031]

[0032] Step S3 includes the following steps:

[0033] The unit volume void is integrated within the volume domain formed by the tunnel face along the construction path of the steep-slope tunnel. This volume domain includes the spatial volume A enclosed by the shield shell boundary ring traveling a distance l along the tunnel axis and the spatial volume B enclosed by the slurry boundary ring traveling a distance l along the tunnel axis. The difference between the integral results of spatial volumes A and B yields the actual construction void G at the tunnel face. e The resulting ground subsidence S z :

[0034]

[0035] The advantages of this invention are: based on the three-dimensional source-sink method, it fully considers the actual construction characteristics of steep-slope tunnels, can accurately predict stratum deformation, and provides a research basis for future calculation methods on stratum deformation caused by asymmetric stratum loss at the horizon. Attached Figure Description

[0036] Figure 1 This is a flowchart of the method for predicting ground deformation caused by construction gaps in steep tunnels according to the present invention.

[0037] Figure 2 This is a construction model diagram of a steep-slope tunnel according to the present invention;

[0038] Figure 3 This is an equivalent diagram of the actual construction gap at the working face of the present invention. Detailed Implementation

[0039] The features and other related features of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments, so as to facilitate understanding by those skilled in the art:

[0040] like Figure 1-3 As shown in the figure, markings 1-3 represent: shield 1, lining 2, and grouting body 3, respectively.

[0041] Example: Figure 1-3 As shown, this embodiment relates to a method for predicting ground deformation caused by construction gaps in steep tunnels. First, a three-dimensional rectangular coordinate system is established, where the origin O, the x-axis, and the y-axis are all located at the ground surface, and the z-axis points vertically downwards. Figure 2 As shown; the prediction method specifically includes the following steps:

[0042] (S1) The tunnel boring machine excavates the tunnel along a steep slope. Based on the three-dimensional source-sink method theory, the solution for the stress increment at any point in space caused by the void per unit volume within a semi-infinite body is obtained, specifically:

[0043] The soil mass is a semi-infinite body bounded by the Earth's surface, encompassing only its lower portion. Assuming the soil mass is an unbounded infinite body, the vertical deformation component at point P(x,y,z) caused by a unit volume void at point F(x0,y0,z0) within this infinite body is:

[0044]

[0045] In the formula: R1=[(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] 1 / 2 ;

[0046] Let there be a point F′(x0,y0,–z0) at the mirror position of point F(x0,y0,–z0). The vertical deformation component at point P(x,y,z) caused by the unit volume void at point F′(x0,y0,–z0) is:

[0047]

[0048] In the formula: R2=[(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 1 / 2 ;

[0049] To conform to the actual boundary conditions (semi-infinite soil in space), the shear stress generated per unit volume of void at the surface is applied in the opposite direction to the surface. The vertical deformation component generated at point P(x,y,z) is then calculated as follows:

[0050]

[0051] In the formula: μ is the Poisson's ratio of the soil; u and t are both independent variables of the function; c and b are the upper and lower limits of integration; R3 = [(xu)] 2 +(yt) 2 +z 2 ] 1 / 2 ;

[0052] Vertical deformation s of soil per unit volume of void space within a semi-infinite body z for:

[0053]

[0054] (S2) Establish a three-dimensional spatial model of the steep-slope tunnel, and combine it with the construction path of the steep-slope tunnel to obtain the actual construction gap G at the tunnel face. e , specifically:

[0055] like Figure 2 As shown, a three-dimensional spatial model of a steeply sloped tunnel with a slope of γ (i.e., the angle between the tunnel axis l2 and the horizontal straight line l1 is γ, with the unit symbol being °) is established. In this model, the downward excavation of the tunnel boring machine is defined as the positive direction and the upward excavation as the negative direction.

[0056] The burial depth at the center O′ of the tunnel face is h (unit symbol is m). Since the burial depth at the x-coordinate on the tunnel axis l2 is a non-constant value that varies with x and γ, this embodiment only discusses the burial depth h(x0) at the point (x0, y0, z0) under a certain slope:

[0057] h(x0) = h + x0tanγ;

[0058] like Figure 3As shown, the actual construction gap G at the working face e Including the tail gap V s and grouting filling V g They are respectively:

[0059] V s =π(R) 2 -r 2 ),

[0060] V g =πλ(1-α1-α2-α3-α4)(R 2 -r 2 ),

[0061] In the formula: R and r are the outer diameters of the tunnel boring machine and the lining 2, respectively; λ is the grouting rate, which can be obtained from the on-site environmental monitoring records. In actual construction, grouting loss is inevitable and is related to the compaction loss coefficient α1, soil loss coefficient α2, transportation loss coefficient α3, and over-excavation loss coefficient α4. The specific value can be determined according to the geological conditions and grouting process.

[0062] Due to the gravity of lining 2 and grouting body 3, the outer edge of lining 2 and the bottom of grouting liquid boundary a will be close to the inner edge of shield 1, and the actual construction gap G at the working face will be... e This can be equivalent to:

[0063]

[0064] (S3) Integrate the unit volume void obtained in step S1 within the volume domain formed by the construction path along the steep slope of the tunnel face. The volume domain includes the spatial volume A enclosed by the shield shell 1 boundary ring traveling a distance l (unit symbol: m) along the tunnel axis l2 and the spatial volume B enclosed by the slurry liquid boundary ring traveling a distance l along the tunnel axis l2. Subtract the integral results of spatial volumes A and B to obtain the actual construction gap G at the tunnel face. e The resulting ground subsidence S z :

[0065]

[0066] In summary, compared with the prior art, the prediction equipment for ground deformation caused by the construction gap of steep-slope tunnels in this embodiment has a solid theoretical foundation. Combined with the actual tunnel excavation path and actual grouting process, it can accurately calculate the ground settlement caused by ground loss in three-dimensional space, and can provide a more realistic answer for predicting ground deformation caused by tunnel construction under unconventional path conditions.

[0067] Although the above embodiments have described the concept and embodiments of the present invention in detail with reference to the accompanying drawings, those skilled in the art will recognize that various improvements and modifications can still be made to the present invention without departing from the scope of the claims, and therefore will not be elaborated here.

Claims

1. A method for predicting ground deformation caused by construction gaps in steep-slope tunnels, characterized in that, The prediction method includes the following steps: (S1) The tunnel boring machine excavates the tunnel along a steep slope. Based on the three-dimensional source-sink method theory, the vertical deformation s of the soil within a semi-infinite body due to the void volume per unit volume is obtained. z ; (S2) Establish a three-dimensional spatial model of the steep slope tunnel, and combine it with the construction path of the steep slope tunnel to obtain the actual construction gap G at the tunnel face. e ; (S3) Integrate the unit volume void within the volume domain formed by the tunnel face along the construction path of the steep-slope tunnel to obtain the actual construction gap G at the tunnel face. e The resulting ground subsidence S z ; Step S1 includes the following steps: Establish a three-dimensional rectangular coordinate system, in which the origin O, the x-axis, and the y-axis are all located on the ground surface, and the z-axis is vertically downward. The soil mass is a semi-infinite body bounded by the Earth's surface, encompassing only its lower portion. Assuming the soil mass is an unbounded infinite body, the vertical deformation component at point P(x,y,z) caused by a unit volume void at point F(x0,y0,z0) within this infinite body is: In the formula: R1=[(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] 12 ; Let there be a point F′(x0,y0,–z0) at the mirror position of point F(x0,y0,–z0). The vertical deformation component at point P(x,y,z) caused by the unit volume void at point F′(x0,y0,–z0) is: In the formula: R2=[(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 12 ; Applying the shear stress generated by the unit volume void at the Earth's surface in the opposite direction to the surface, the vertical deformation component generated at point P(x,y,z) is calculated as follows: In the formula: μ is the Poisson's ratio of the soil; u and t are both independent variables of the function; c and b are the upper and lower limits of integration variables; R3=[(x-u) 2 +(y-t) 2 +z 2 ] 12 ; The vertical deformation s of the soil within the semi-infinite body due to the void volume per unit volume z for: Step S2 includes the following steps: A three-dimensional spatial model of a tunnel with a steep gradient of γ is established, where downward excavation by the tunnel boring machine is the positive direction and upward excavation is the negative direction. The burial depth of the center O′ of the working face is h, and the burial depth h(x0) at point (x0, y0, z0) is: h(x0) = h + x0tanγ; The actual construction gap at the working face e Including the tail gap V s and grouting filling V g They are respectively: V s =π(R 2 -r 2 ), V g =pl(1-α1-α2-α3-α4)(R 2 -r 2 ), In the formula: R and r are the outer diameters of the tunnel boring machine and the lining, respectively; λ is the grouting rate; α1 is the compaction loss coefficient; α2 is the soil loss coefficient; α3 is the conveying loss coefficient; α4 is the over-excavation loss coefficient; Due to the gravity of the lining and grout, the outer edge of the lining and the bottom of the grout will be close to the inner edge of the shield. The actual construction gap G at the working face... e for: Step S3 includes the following steps: The unit volume void is integrated within the volume domain formed by the tunnel face along the construction path of the steep-slope tunnel. This volume domain includes the spatial volume A enclosed by the shield shell boundary ring traveling a distance l along the tunnel axis and the spatial volume B enclosed by the slurry boundary ring traveling a distance l along the tunnel axis. The difference between the integral results of spatial volumes A and B yields the actual construction void G at the tunnel face. e The resulting ground subsidence S z :

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