A method for predicting ground stress increment caused by TBM slope change construction gap

Abstract

The application discloses a kind of TBM variable slope construction gap caused by stratum stress increment prediction method, and prediction method includes the following steps: TBM is excavated tunnel along large gradient construction path, based on three-dimensional source and sink method theory, the stress increment solution of any point in space caused by unit volume gap in semi-infinite body is obtained;Three-dimensional space model of large gradient tunnel is established, combined with the construction path of large gradient tunnel, the strata loss percentage produced in the excavation of TBM is determined, and the actual construction gap of large gradient tunnel is obtained;Unit volume gap is integrated in the volume domain of the actual construction gap of large gradient tunnel, and the stratum stress increment caused by the actual construction gap of large gradient tunnel is obtained.The application has the advantages that: it is suitable for three-dimensional space working condition of soil loss gap, taking the example of excavation along large gradient path, the strata loss percentage is a non-constant value that changes with buried depth, and the change of surrounding stratum stress field caused by three-dimensional construction gap can be accurately calculated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel engineering, and particularly relates to a method for predicting ground stress increment caused by construction gap of TBM (Tunnel Boring Machine) with slope change. BACKGROUND

[0002] The excavation path of a TBM (Tunnel Boring Machine) is not necessarily a straight line in a horizontal plane, and in order to meet the site condition restrictions, the TBM has to be excavated along a large slope path uphill and downhill. During the tunnel excavation process, the ground loss will cause the surrounding rock of the TBM excavation boundary to move towards the tunnel center, and especially for a large slope tunnel, the ground loss rate changes with the tunnel depth. During the construction process, the construction gap caused by the ground loss will inevitably disturb the surrounding ground. At present, the calculation object of the prediction program of the ground disturbance caused by the TBM excavation is mostly a straight tunnel in a plane, and there are few reports on the calculation program of the ground stress increment caused by the ground loss for a large slope tunnel. Therefore, there is an urgent need for a method for predicting the ground stress increment caused by the construction gap of the TBM with slope change. SUMMARY

[0003] The present application aims at solving the above problems, and provides a method for predicting the ground stress increment caused by the construction gap of the TBM with slope change. Based on the three-dimensional source-sink method principle and the triple integral principle, the method can accurately calculate the ground stress caused by the construction gap, in combination with the actual three-dimensional space characteristics of the large slope tunnel.

[0004] The object of the present application is achieved by the following technical solutions.

[0005] The present application relates to the technical field of tunnel engineering, and particularly relates to a method for predicting ground stress increment caused by construction gap of TBM (Tunnel Boring Machine) with slope change.

[0006] (S1) The TBM excavates a tunnel along a large slope construction path, and based on the three-dimensional source-sink method theory, a stress increment solution of a unit volume gap at any point in space is obtained;

[0007] (S2) A three-dimensional space model of the large slope tunnel is established, and in combination with the construction path of the large slope tunnel, the ground loss percentage generated by the TBM during the excavation is determined, and the actual construction gap of the large slope tunnel is obtained;

[0008] (S3) The unit volume gap is integrated in the volume domain of the actual construction gap of the large slope tunnel, and the ground stress increment caused by the actual construction gap of the large slope tunnel is obtained.

[0009] Step S1 comprises the following steps:

[0010] A three-dimensional rectangular coordinate system is established, and the coordinate origin O, the x-axis and the y-axis of the three-dimensional rectangular coordinate system are located on the ground surface, and the z-axis is vertically downward;

[0011] The soil body is a semi-infinite body with the ground surface as a boundary and only containing a lower part of the semi-infinite body, and it is assumed that the soil body is an infinite body without a boundary, and a unit volume void at a point F(x0, y0, z0) in the infinite body causes displacement components in the x, y and z directions of a point P(x, y, z):

[0012]

[0013]

[0014]

[0015] In the formula, r1 = [(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] 1 / 2 ;

[0016] A point F'(x0, y0, -z0) is arranged at a mirror image position of the point F(x0, y0, z0), and a unit volume void at the point F'(x0, y0, -z0) causes displacement components in the x, y and z directions of the point P(x, y, z):

[0017]

[0018] In the formula, r2 = [(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 1 / 2 ;

[0019] Based on the basic equations of elastic mechanics, strain and stress solutions caused by the unit volume void are obtained:

[0020]

[0021]

[0022] In the formula, G is the shear modulus of the stratum, and μ is the Poisson's ratio of the stratum;

[0023] The unit volume void causes stresses in the x, y and z directions:

[0024]

[0025]

[0026]

[0027] The shear stress generated by the unit volume of void at the surface acts on the surface in the opposite direction, and the stress component generated by point P(x, y, z) is obtained:

[0028]

[0029]

[0030]

[0031] In the formula: b, c, u, t are function arguments; r3=[(x-u) 2 +(y-t) 2 +z 2 ] 1 / 2 ;

[0032] Based on the principle of superposition, the stress increment of any point caused by the unit volume of void is obtained:

[0033]

[0034] Step S2 includes the following steps:

[0035] A three-dimensional space model of the large slope tunnel with a slope of γ is established, wherein the downward excavation of the TBM is the positive direction and the upward excavation is the negative direction;

[0036] The center O' of the tunnel face of the large slope tunnel is at a depth of h, and the depth h(x0) at point (x0, y0, z0) is:

[0037] h(x0)=h+x0tanγ;

[0038] The ground loss percentage η(x0) at point (x0, y0, z0) is:

[0039]

[0040] In the formula: η is the maximum ground loss percentage;

[0041] The three-dimensional construction void volume generated within the unit length range along the large slope construction path is:

[0042] V s (x0)=πR 2 η(x0),

[0043] In the formula: R is the excavation outer diameter of the TBM;

[0044] The actual construction gap of the large slope tunnel is:

[0045]

[0046] Step S3 comprises the following steps:

[0047] The unit volume void is integrated in the volume domain of the actual construction gap of the large slope tunnel, the volume domain includes the space volume A surrounded by the TBM boundary circular ring along the tunnel axis for l distance and the space volume B surrounded by the boundary circular ring after the surrounding rock moves along the tunnel axis for l distance, the integral results of the space volume A and the space volume B are subtracted, and the ground stress increment caused by the actual construction gap of the large slope tunnel is obtained:

[0048]

[0049]

[0050]

[0051] The advantages of the present application are: suitable for three-dimensional space working conditions of soil loss gap, taking the example of tunneling along the large slope path, the ground loss percentage is a non-constant value that changes with the burial depth, and the change of the surrounding ground stress field caused by the three-dimensional construction gap can be accurately calculated. BRIEF DESCRIPTION OF DRAWINGS

[0052] Fig. 1 The flow chart of the prediction method of the ground stress increment caused by the TBM slope change construction gap of the present application;

[0053] Fig. 2 The large slope tunnel construction model of the present application. DETAILED DESCRIPTION

[0054] The features and other related features of the present application are further described in detail below by embodiments combined with the drawings, so as to facilitate the understanding of the same by the same industry technical personnel:

[0055] Embodiment: as shown in the figure, the present embodiment relates to a prediction method of the ground stress increment caused by the TBM slope change construction gap, first, a three-dimensional rectangular coordinate system is established, the coordinate origin O, x-axis and y-axis are located on the ground surface, and the z-axis is vertically downward, as shown in the figure; the prediction method specifically comprises the following steps: Figs. 1-2 Fig. 2 (S1) TBM excavates the tunnel along the large slope construction path, based on the three-dimensional source and sink method theory, the stress increment solution of the unit volume void at any point in space is obtained, specifically:

[0056] (S1) TBM excavates the tunnel along the large slope construction path, based on the three-dimensional source and sink method theory, the stress increment solution of the unit volume void at any point in space is obtained, specifically:

[0057] ​The soil body is a semi-infinite body with the ground surface as a boundary and only containing the lower part of the semi-infinite body. Assuming that the soil body is an infinite body without a boundary, a unit volume void at a point F(x0, y0, z0) in the infinite body causes displacement components in the x, y and z directions at a point P(x, y, z) as follows:

[0058]

[0059]

[0060]

[0061] wherein r1 = [(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] 1 / 2 ;

[0062] A point F'(x0, y0, -z0) is set at the mirror image position of the point F(x0, y0, z0). A unit volume void at the point F'(x0, y0, -z0) causes displacement components in the x, y and z directions at the point P(x, y, z) as follows:

[0063]

[0064] wherein r2 = [(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 1 / 2 ;

[0065] Based on the basic equations of elastic mechanics, the strain and stress solutions caused by a unit volume void are obtained as follows:

[0066]

[0067]

[0068] wherein G is the shear modulus of the stratum; and μ is the Poisson's ratio of the stratum.

[0069] The stresses in the x, y and z directions caused by a unit volume void are as follows:

[0070]

[0071]

[0072]

[0073] In order to meet the actual semi-infinite body boundary conditions, the shear stress generated by unit volume of void on the ground surface is applied to the ground surface in the opposite direction, and the stress components generated by point P(x, y, z) are obtained:

[0074]

[0075]

[0076]

[0077] In the formula, b, c, u, t are function arguments; r3 = [(x-u) 2 +(y-t) 2 +z 2 ] 1 / 2 ;

[0078] Based on the principle of superposition, the stress increment of any point caused by unit volume of void is obtained:

[0079]

[0080] (S2) Establish a three-dimensional space model of the large slope tunnel, determine the ground loss percentage generated by the TBM in the tunneling process combined with the construction path of the large slope tunnel, and obtain the actual construction gap of the large slope tunnel, specifically:

[0081] As shown in Fig. 2 , a three-dimensional space model of a large slope tunnel with a slope of γ (i.e., the angle between the tunnel axis l2 and the horizontal straight line l1 is γ, and the unit symbol is °) is established, wherein it is agreed that the downward tunneling of the TBM is the positive direction and the upward tunneling is the negative direction;

[0082] The center O' of the tunnel face of the large slope tunnel is at a depth of h (unit symbol: m). Since the depth at the x coordinate on the tunnel axis l2 varies with x and γ, this embodiment only discusses the depth h(x0) at point (x0, y0, z0) under a certain slope:

[0083] h(x0) = h + x0tanγ;

[0084] Assuming that the ground loss percentage is a non-constant value that varies with x and γ after the TBM tunneling without timely support, this embodiment only discusses the ground loss percentage η(x0) at point (x0, y0, z0) under a certain slope:

[0085]

[0086] In the formula, η is the maximum ground loss percentage, which is related to the engineering geological conditions, and also related to factors such as construction technology;

[0087] The three-dimensional construction gap volume generated along the unit length range of the large slope construction path is:

[0088] V s (x0)=πR 2 η(x0),

[0089] In the formula, R is the excavation outer diameter of the TBM;

[0090] Without considering the timely grouting and anchor reinforcement, the gap of the excavation boundary (for example, the position of the surrounding rock vault) moving to the center of the working face is:

[0091]

[0092] (S3) The unit volume gap obtained in step S1 is subjected to an integral operation in the volume domain of the actual construction gap of the large slope tunnel, the volume domain includes the space volume A surrounded by the TBM boundary circle ring advancing l (unit symbol is m) along the tunnel axis l2 and the space volume B surrounded by the boundary circle ring after the surrounding rock moves advancing l along the tunnel axis l2, and the integral results of the space volume A and the space volume B are subtracted to obtain the calculation formula of the ground stress increment of the surrounding rock along the x axis, the y axis and the z axis caused by the actual construction gap of the TBM, respectively:

[0093]

[0094]

[0095]

[0096] In order to characterize the three-dimensional spatial distribution of the stress field around the tunnel, the calculation path is selected as follows: on the one hand, a straight line l3 parallel to the large slope tunnel axis l2 is taken as the calculation path, and the radial distance r0 between the tunnel axis l2 and the straight line l3 is nR (n=2, 3, 4, …); on the other hand, a certain vertical section a is selected on the large slope tunnel axis l2, and the intersection point of the vertical section a and the tunnel axis l2 is taken as the center of the circle, and a circle (radius r0=nR, n=2, 3, 4, …) is drawn in the section a, and the hoop distribution of the stress field at different r0 is calculated.

[0097] In summary, compared with the prior art, the embodiment is based on the three-dimensional source and sink method principle and the triple integral principle, and combines the actual three-dimensional spatial position of the construction gap, so that the additional ground stress can be accurately predicted, and the embodiment has the advantages of high calculation efficiency, easy parameter value selection, conformity to engineering practice and the like.

[0098] Although the above embodiments have been described with reference to the accompanying drawings, it is to be understood that the present application is not limited to the embodiments disclosed herein, but that various modifications and changes can be made thereto without departing from the scope of the application as set forth in the claims.

Claims

1. A method for predicting ground stress increment caused by TBM slope construction gap, characterized in that, The prediction method comprises the following steps: (S1) A TBM excavates a tunnel along a large-gradient construction path, and based on a three-dimensional source-sink method theory, a stress increment solution of any point in space caused by a unit volume void in a semi-infinite body is obtained; (S2) A three-dimensional space model of the large-gradient tunnel is established, and in combination with the construction path of the large-gradient tunnel, a stratum loss percentage generated by the TBM in excavation is determined, and an actual construction gap of the large-gradient tunnel is obtained; (S3) An integral operation is performed on the unit volume void in a volume domain of the actual construction gap of the large-gradient tunnel, and a stratum stress increment caused by the actual construction gap of the large-gradient tunnel is obtained; Step S1 comprises the following steps: A three-dimensional rectangular coordinate system is established, and a coordinate origin O, an x-axis and a y-axis in the three-dimensional rectangular coordinate system are located on a ground surface, and a z-axis is vertically downward; A soil body is a semi-infinite body with the ground surface as a boundary and only including a lower part of the semi-infinite body, and it is assumed that the soil body is an infinite body without a boundary, and displacement components of a point P(x, y, z) in a direction along coordinate axes x, y and z caused by a unit volume void at a point F(x0, y0, z0) in the infinite body are: where: r1 = [(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] 1 / 2 ; A point F'(x0, y0, -z0) is arranged at a mirror image position of the point F(x0, y0, z0), and displacement components of the point P(x, y, z) in the direction along the coordinate axes x, y and z caused by a unit volume void at the point F'(x0, y0, -z0) are: where: r2= [(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 1 / 2 ; Based on basic equations of elastic mechanics, a strain and a stress solution generated by the unit volume void are obtained: In the formula, G is a stratum shear modulus, and μ is a stratum Poisson's ratio; Stresses generated by the unit volume void in the direction along the x-axis, the y-axis and the z-axis are: A shear stress generated by the unit volume void on the ground surface is applied to the ground surface in a reverse direction, and stress components generated by the point P(x, y, z) are obtained: wherein: b, c, u, t are function arguments; r3 = [(x-u) 2 +(y-t) 2 +z 2 ] 1 / 2 ; Based on a superposition principle, a stress increment of any point caused by the unit volume void is obtained: Step S2 comprises the following steps: A three-dimensional space model of the large-gradient tunnel with a gradient γ is established, wherein a downward excavation of the TBM is a positive direction, and an upward excavation is a negative direction; A center O' of a tunnel face of the large-gradient tunnel is located at a depth h, and a depth h(x0) of a point (x0, y0, z0) is: h(x0) = h + x0 tan γ; A stratum loss percentage η(x0) of the point (x0, y0, z0) is: In the formula, η is a maximum stratum loss percentage; A three-dimensional construction void volume generated in a unit length range along the large-gradient construction path is: V s (x0) = πR 2 η(x0), In the formula, R is an excavation outer diameter of the TBM; An actual construction gap of the large-gradient tunnel is:

2. The method of claim 1, wherein, Step S3 comprises the following steps: An integral operation is performed on the unit volume void in a volume domain of the actual construction gap of the large-gradient tunnel, the volume domain includes a space volume A surrounded by a TBM boundary circular ring along a tunnel axis line for an l distance and a space volume B surrounded by a boundary circular ring of surrounding rock after movement along the tunnel axis line for the l distance, and a difference between integral results of the space volume A and the space volume B is obtained, and a stratum stress increment caused by the actual construction gap of the large-gradient tunnel is obtained:

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