Method for predicting stress field change of surrounding soil caused by shield tunneling along curved path

Abstract

The present invention discloses a method for predicting changes in the stress field of the surrounding soil caused by shield tunneling along a curved path, comprising the following steps: (1) using the principle of a three-dimensional source-sink method to obtain a solution to the stress increment at any point in space caused by a unit volume gap in a semi-infinite body; (2) determining the amount of stratum loss during actual tunneling based on the characteristics of shield tunneling along the curved path; and (3) developing a calculation program for changes in the stress field of the surrounding soil caused by the actual stratum loss along the axial direction and the direction of the annular excavation surface when the shield tunneling along the curved path is tunneled, so as to obtain the stratum stress changes along the axial direction and the stratum stress changes along the annular excavation surface when the shield tunneling along the curved path. The advantages of the present invention are that it is applicable to working conditions where the soil loss gap is a three-dimensional space. For example, when tunneling along a curved path, curved over-excavation is required during construction. By using the prediction program of the present invention, the changes in the stress field of the surrounding soil caused by the three-dimensional over-excavation gap can be accurately calculated.

Description

Technical Field

[0001] The invention belongs to the technical field of shield tunneling and underground engineering, and particularly relates to a method for predicting changes in stress field of surrounding soil caused by shield tunneling along a curved path. Background Art

[0002] During subway construction, the tunneling path of a shield machine is not necessarily entirely straight. To meet site constraints, the shield machine inevitably tunnels along curved paths. During shield tunneling, a non-uniform gap exists between the outer wall and the boundary soil layer at the moment the tail segment is released. Especially for curved tunnels, overexcavation gaps are unavoidable to ensure smooth tunneling. During construction, the gaps caused by overexcavation in the curved section inevitably disturb the surrounding strata. Current prediction programs for ground disturbance caused by shield tunneling are designed for straight tunnels, but few have been reported for curved tunnels, particularly those that predict ground stress caused by soil loss. Furthermore, predictions of ground disturbance caused by shield tunneling are mostly limited to its impact on soil displacement. Few calculation programs or methods can predict its impact on ground stress. Since stress changes are the primary cause of ground displacement, there is an urgent need for convenient, fast, and reliable calculation programs to predict the stress field changes in the surrounding soil caused by shield tunneling along curved paths. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for predicting changes in the stress field of the surrounding soil caused by shield tunneling along a curved path based on the shortcomings of the above-mentioned prior art. Taking curved path tunneling as an example, the method uses a calculation program to develop a calculation program for the changes in the stress field of the surrounding soil along the axis direction and the direction of the annular excavation surface caused by the actual stratum loss when the shield tunneling along the curved path, so as to obtain the stratum stress changes along the axis direction and the stratum stress changes along the annular excavation surface when the shield tunneling along the curved path.

[0004] The purpose of the present invention is achieved by the following technical solutions:

[0005] A method for predicting changes in the stress field of surrounding soil caused by shield tunneling along a curved path, characterized in that the method comprises the following steps:

[0006] (1) Using the principle of three-dimensional source-sink method, we can obtain the stress increment at any point in space caused by the unit volume void in a semi-infinite body;

[0007] (2) Determine the amount of ground loss during actual tunneling based on the characteristics of shield tunneling along a curved path;

[0008] (3) Develop a calculation program for the changes in the stress field of the surrounding soil along the axis and the direction of the ring excavation surface caused by the actual stratum loss when the shield tunneling along the curved path, so as to obtain the stratum stress changing along the axis direction and the stratum stress changing along the ring excavation surface when the shield tunneling along the curved path.

[0009] 1. A method for predicting changes in the stress field of surrounding soil caused by shield tunneling along a curved path according to claim 1, characterized in that step (1) includes the following steps:

[0010] (1.1) Assuming that the soil is an infinite body without boundaries, give the displacement component S at point P(x, y, z) caused by the unit volume void at the midpoint F(x0, y0, z0) of the infinite body: k1 :

[0011]

[0012] Where:

[0013] k is the function's independent variable, which can be x, y, or z;

[0014] (k–k0)=one of (x–x0), (y–y0), (z–z0);

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

[0016] (1.2) Obtain the displacement component of the volume expansion at point P(x,y,z) of equal magnitude at the mirror image point F′(x0,y0,–z0) of point F(x0,y0,z0):

[0017]

[0018] Where:

[0019] m is x or y;

[0020] (m–m0)=(x–x0) or (y–y0);

[0021] r2=[(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 1 / 2 ;

[0022] (1.3) Given the basic equations of elasticity, we can obtain the strain and stress solutions generated in steps (1.1) and (1.2):

[0023]

[0024]

[0025] Where:

[0026] k is the function variable, which can be x, y or z;

[0027] S k2 Citation S m2 The calculation formula of

[0028] m = x, or y;

[0029] G is the soil shear modulus;

[0030] μ is the Poisson's ratio of soil;

[0031] (1.4) The stress calculation program along the m-axis generated by the above two steps is obtained:

[0032]

[0033] in:

[0034] The m-axis refers to the x-axis or y-axis;

[0035] (m,n)=(x,y), or (y,x);

[0036] The two steps refer to the solution of the stress components at any point caused by the gaps in the infinite body and its mirror image gap. In order to meet the actual boundary conditions, that is, the semi-infinite body conditions, the shear stress (Gγ) generated on the surface in the first two steps should be xz ; Gγ yz ) acts on the surface in the opposite direction, the stress components generated can be obtained:

[0037]

[0038]

[0039] Where:

[0040] b, c, u, and t are all function variables;

[0041] r3=[(xu) 2 +(yt) 2 +z 2 ] 1 / 2 ;

[0042] The sum of the solutions in the above three steps is the solution to the stress increment at any point caused by a gap with a radius of 1. Therefore, the stress increment generated by the gap per unit volume is:

[0043] (m=x or y).

[0044] Step (2) includes the following steps: in order to meet the purpose of turning in the curved section, the inner side of the curve needs to be over-excavated when the shield is yawed and advanced. Assuming that the existence of the hinged device of the shield divides the shield body into a front shield and a rear shield, the over-excavation of the curved section is sufficient to meet the shield tail covering 2 rings of segments, and the ring width of the segment is b1. At the same time, considering the timely support of the rear shield after excavation, the soil displacement is subject to three-dimensional constraints, so the over-excavation of the excavation surface should be reduced. According to experience, it is taken as 1 / 3, and the calculation formula of the over-excavation gap ω of the excavation surface is:

[0045]

[0046] Where:

[0047] Q is the radius of curvature of the curved tunnel axis;

[0048] R is the outer diameter of the shield;

[0049] b1 is the segment ring width.

[0050] Step (3) includes the following steps: Under the influence of the curve over-excavation, the stress increment calculation procedure caused by the surrounding soil is:

[0051]

[0052] Where:

[0053] θ is the angle between the line connecting the center of the cross section of the curved tunnel and its projection point on the z-axis and the oxz plane in the three-dimensional rectangular coordinate system;

[0054] q is the function variable;

[0055] l is the excavation length of the shield;

[0056] h is the buried depth of the tunnel axis.

[0057] The method for characterizing the three-dimensional spatial distribution of the stress field around the tunnel is as follows: assuming that the axis of the curved tunnel excavation is an arc with a radius of Q in a horizontal plane, the selected calculation path is as follows: on the one hand, in the horizontal plane where the axis of the curved tunnel excavation is located, a curve that is a concentric arc with the axis of the curved tunnel excavation is taken as the calculation path, and the radial distance r0 between the two curves is nR, where n = 2, 3, 4, ...; the calculation path is located outside the curved tunnel; on the other hand, a specific section is selected along the axis of the curved tunnel excavation, and the intersection of the specific section and the axis of the curved tunnel excavation is used as the center of the circle. A circle with a radius of r0 = nR, where n = 2, 3, 4, ... is drawn on the specific section; the circumferential distribution of the stress field at each point on the circumference is calculated under different r0 conditions.

[0058] The advantages of the present invention are: compared with the existing technology, the present invention is applicable to the working condition where the soil loss gap is three-dimensional. Taking excavation along a curved path as an example, curved over-excavation is required during construction. By using the prediction program described in the present invention, the changes in the stress field of the surrounding soil caused by the three-dimensional over-excavation gap can be accurately calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a flow chart for predicting changes in the stress field of the surrounding soil caused by the shield tunneling along a curved path in the present invention;

[0060] Figure 2 This is a schematic diagram of the curved shield tunnel excavation model and calculation path in the present invention. DETAILED DESCRIPTION

[0061] The features of the present invention and other related features are further described in detail below through embodiments in conjunction with the accompanying drawings to facilitate understanding by those skilled in the art:

[0062] Example:

[0063] like Figure 1 Figure 2 shows a schematic diagram of the curved shield tunneling model and calculation path. Assuming the tunneling axis is a circular arc with a radius of Q in the horizontal plane, the calculation path is selected as follows: First, within the horizontal plane containing the curved tunnel axis, a concentric curve is selected as the calculation path (hereinafter referred to as the axis direction). The radial distance r0 between the two curves is nR (n = 2, 3, 4, ...). This calculation path is located outside the curved tunnel. Second, a specific section is selected along the tunnel axis, and its intersection with the tunnel axis is used as the center. A circle is drawn around this section, and the circumferential distribution of the stress field at each point on the circumference is calculated for different r0 values.

[0064] like Figure 1 、 2 As shown, this embodiment specifically relates to a method for predicting changes in the stress field of surrounding soil caused by shield tunneling along a curved path, including the following steps:

[0065] (1) Using the principle of three-dimensional source-sink method, we can obtain the stress increment solution at any point in space caused by the unit volume void in the semi-infinite body. Specifically:

[0066] (1.1) Assuming that the soil is an infinite body without boundaries, give the displacement component S at point P(x, y, z) caused by the unit volume void at the midpoint F(x0, y0, z0) of the infinite body: k1 :

[0067]

[0068] Where:

[0069] k is the function's independent variable, which can be x, y, or z;

[0070] (k–k0)=one of (x–x0), (y–y0), (z–z0);

[0071] r1=[(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] 1 / 2 .

[0072] (1.2) Obtain the displacement component of the volume expansion at point P(x,y,z) of equal magnitude at the mirror image point F′(x0,y0,–z0) of point F(x0,y0,z0):

[0073]

[0074] Where:

[0075] m is x or y; it should be noted that, in order to omit multiple expressions of the formula, the letter k mentioned above is used to represent x, y, or z, and m here represents x or y;

[0076] (m–m0)=(x–x0) or (y–y0);

[0077] r2=[(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 1 / 2 .

[0078] (1.3) Given the basic equations of elasticity, we can obtain the strain and stress solutions generated in steps (1.1) and (1.2):

[0079]

[0080]

[0081] Where:

[0082] k is the function's independent variable, which can be x, y, or z;

[0083] S k2 Citation S m2 The calculation formula of

[0084] m = x, or y;

[0085] G is the soil shear modulus;

[0086] μ is the Poisson's ratio of the soil.

[0087] (1.4) The stress calculation program along the m-axis generated by the above two steps is obtained:

[0088]

[0089] in:

[0090] The m-axis refers to the x-axis or y-axis;

[0091] (m,n)=(x,y), or (y,x);

[0092] The above two steps refer to the solution of the stress components at any point caused by the gaps in the infinite body and its mirror image gap. In order to meet the actual boundary conditions, that is, the semi-infinite body conditions, the shear stress (Gγ) generated on the surface in the first two steps should be xz ; Gγ yz ) acts on the surface in the opposite direction, the stress components generated can be obtained:

[0093]

[0094]

[0095] Where:

[0096] b, c, u, and t are all function variables;

[0097] r3=[(xu) 2 +(yt) 2 +z 2 ] 1 / 2 ;

[0098] The sum of the solutions in the above three steps is the solution to the stress increment at any point caused by a gap with a radius of 1. Therefore, the stress increment generated by the gap per unit volume is:

[0099] (m=x, or y).

[0100] (2) According to the characteristics of shield tunneling along the curved path, the amount of ground loss during the actual tunneling period is determined, specifically:

[0101] To meet the purpose of turning in the curved section, the inner side of the curve needs to be over-excavated when the shield machine is yawed. Assuming that the shield machine body is divided into the front shield and the rear shield by the existence of the articulated device, the over-excavation of the curved section is sufficient to meet the shield tail covering two rings of segments, and the ring width of the segment is b1. At the same time, considering the timely support of the rear shield after excavation, the soil displacement is subject to three-dimensional constraints. Therefore, the over-excavation of the excavation surface should be reduced. According to experience, it is taken as 1 / 3. The calculation formula of the over-excavation gap ω of the excavation surface is:

[0102]

[0103] Where:

[0104] Q is the radius of curvature of the curved tunnel axis;

[0105] R is the outer diameter of the shield;

[0106] b1 is the segment ring width.

[0107] This embodiment provides a program for predicting changes in the stress field of the surrounding soil caused by shield tunneling along a curved path. The program has a solid theoretical basis and studies the soil stress estimation program caused by the curved over-excavation gap during the construction of a curved shield tunnel. The program combines the actual three-dimensional spatial characteristics of the curved tunnel, and the calculation is relatively convenient, fast, and reliable.

[0108] During the excavation of a curved shield tunnel, the tunnel alignment determines the complexity of the three-dimensional space of soil loss, which can easily cause stress changes in the soil around the curved tunnel, thus affecting construction. Therefore, it is necessary to pre-estimate the impact of the actual over-excavation gap on soil stress. Figure 2 As shown, it is a flow chart of the program for predicting soil stress around a curved tunnel caused by the curved over-excavation gap described in this embodiment.

[0109] (3) Develop a calculation program for the changes in the stress field of the surrounding soil along the axis and the direction of the excavation surface caused by the actual stratum loss when the shield tunneling along the curved path, so as to obtain the stratum stress changes along the axis and the stratum stress changes around the excavation surface when the shield tunneling along the curved path, specifically:

[0110] Using the triple integral principle, the calculation procedure for the stress increment caused by the surrounding soil under the influence of curve over-excavation can be obtained as follows:

[0111]

[0112] Where:

[0113] θ is the angle between the line connecting the center of the cross section of the curved tunnel and its projection point on the z-axis and the oxz plane in the three-dimensional rectangular coordinate system;

[0114] q is the function variable;

[0115] l is the excavation length of the shield;

[0116] h is the buried depth of the tunnel axis.

[0117] Compared with the existing technology, the program provided in this embodiment is based on the three-dimensional source-sink method principle and the triple integral principle to predict the changes in the stress field of the surrounding soil caused by the shield tunneling along a curved path. It is combined with the actual three-dimensional spatial position of the over-excavation gap, and can more accurately predict the additional stress of the stratum. It has the advantages of high computational efficiency, easy selection of corresponding parameters, and compliance with engineering practice.

[0118] The above-described embodiments merely illustrate several implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A method for predicting the stress field changes of the surrounding soil caused by shield tunneling along a curved path, characterized in that The method comprises the following steps: (1) Using the principle of three-dimensional source-sink method, we can obtain the stress increment at any point in space caused by the unit volume void in a semi-infinite body; (2) Determine the amount of ground loss during actual tunneling based on the characteristics of shield tunneling along a curved path; (3) Develop a calculation program for the changes in the stress field of the surrounding soil along the axis and the direction of the excavation surface caused by the actual stratum loss when the shield tunneling along the curved path, so as to obtain the stratum stress changing along the axis and the stratum stress changing around the excavation surface when the shield tunneling along the curved path; Step (1) includes the following steps: (1.1) Assuming that the soil is an infinite body without boundaries, give the displacement component S at the point P(x, y, z) caused by the unit volume void at the midpoint F(x0, y0, z0) of the infinite body: k1 : Where: k is the function variable, which can be x, y or z; (k–k0)=one of (x–x0), (y–y0), (z–z0); r1=[(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] 1 / 2 ; (1.2) Obtain the displacement component of the volume expansion at point P(x,y,z) of equal magnitude at the mirror image point F′(x0,y0,–z0) of point F(x0,y0,z0): Where: m is x or y; (m–m0)=(x–x0) or (y–y0); r2=[(x-x0) 2 +(y-y0) 2 +(z+z0) 2 ] 1 / 2 ; (1.3) Given the basic equations of elasticity, we can obtain the strain and stress solutions generated in steps (1.1) and (1.2): Where: k is the function variable, which can be x, y or z; S k2 Citation S m2 The calculation formula of m = x, or y; G is the soil shear modulus; μ is the Poisson's ratio of soil; (1.4) The stress calculation program along the m-axis generated by the above two steps is obtained: in: The m-axis refers to the x-axis or y-axis; (m,n)=(x,y), or (y,x); The two steps refer to the solution of the stress components at any point caused by the gaps in the infinite body and its mirror image gap. In order to meet the actual boundary conditions, that is, the semi-infinite body conditions, the shear stress (Gγ) generated on the surface in the first two steps should be xz ; Gγ yz ) acts on the surface in the opposite direction, the stress components generated can be obtained: Where: b, c, u, and t are all function variables; r3=[(x-u) 2 +(y-t) 2 +z 2 ] 1 / 2 ; The sum of the solutions in the above three steps is the solution to the stress increment at any point caused by a gap with a radius of 1. Therefore, the stress increment generated by the gap per unit volume is: (m=x, or y).

2. A method for predicting changes in the stress field of the surrounding soil caused by shield tunneling along a curved path according to claim 1, characterized in that Step (2) includes the following steps: in order to meet the purpose of turning in the curved section, the inner side of the curve needs to be over-excavated when the shield is yawed and advanced. Assuming that the existence of the hinged device of the shield divides the shield body into a front shield and a rear shield, the over-excavation of the curved section is sufficient to meet the shield tail covering 2 rings of segments, and the ring width of the segment is b1. At the same time, considering the timely support of the rear shield after excavation, the soil displacement is subject to three-dimensional constraints, so the over-excavation of the excavation surface should be reduced. According to experience, it is taken as 1 / 3, and the calculation formula of the over-excavation gap ω of the excavation surface is: Where: Q is the radius of curvature of the curved tunnel axis; R is the outer diameter of the shield; b1 is the segment ring width.

3. A method for predicting changes in the stress field of surrounding soil caused by shield tunneling along a curved path according to claim 2, characterized in that Step (3) includes the following steps: Under the influence of the curve over-excavation, the stress increment calculation procedure caused by the surrounding soil is: Where: θ is the angle between the line connecting the center of the cross section of the curved tunnel and its projection point on the z-axis and the oxz plane in the three-dimensional rectangular coordinate system; q is the function variable; l is the excavation length of the shield; h is the buried depth of the tunnel axis.

4. A method for predicting changes in the stress field of surrounding soil caused by shield tunneling along a curved path according to claim 3, characterized in that The method for characterizing the three-dimensional spatial distribution of the stress field around the tunnel is as follows: assuming that the axis of the curved tunnel excavation is an arc with a radius of Q in a horizontal plane, the selected calculation path is as follows: on the one hand, in the horizontal plane where the axis of the curved tunnel excavation is located, a curve that is a concentric arc with the axis of the curved tunnel excavation is taken as the calculation path, and the radial distance r0 between the two curves is nR, where n = 2, 3, 4, ...; the calculation path is located outside the curved tunnel; on the other hand, a specific section is selected along the axis of the curved tunnel excavation, and the intersection of the specific section and the axis of the curved tunnel excavation is used as the center of the circle. A circle with a radius of r0 = nR, where n = 2, 3, 4, ... is drawn on the specific section; the circumferential distribution of the stress field at each point on the circumference is calculated under different r0 conditions.

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