CN114417451A - Method for predicting stress field change of surrounding soil body caused by shield tunneling along curved path - Google Patents

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

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CN114417451A
CN114417451A CN202111524883.2A CN202111524883A CN114417451A CN 114417451 A CN114417451 A CN 114417451A CN 202111524883 A CN202111524883 A CN 202111524883A CN 114417451 A CN114417451 A CN 114417451A
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李少华
黄昌富
姚铁军
赵中华
栾焕强
张帆舸
岳粹洲
田国文
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China Railway 15th Bureau Group Co Ltd
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Abstract

The invention discloses a method for predicting the change of a stress field of a surrounding soil body caused by tunneling of a shield along a curved path, which comprises the following steps: (1) obtaining a stress increment solution of any point in space caused by a unit volume gap in a semi-infinite body by using a three-dimensional source-sink method principle; (2) determining the stratum loss amount during the actual tunneling period according to the tunneling characteristic of the shield along the curved path; (3) and developing a calculation program of the change of the stress field of the surrounding soil body along the axial direction and the direction of the annular excavation surface caused by the actual stratum loss amount when the shield tunnels along the curved path so as to obtain the stratum stress changed along the axial direction and the stratum stress changed along the annular excavation surface when the shield tunnels along the curved path. The invention has the advantages that: the method is suitable for the working condition that the soil body loss gap is a three-dimensional space, taking tunneling along a curved path as an example, curve overexcavation is needed during construction, and the change of the stress field of the surrounding soil body caused by the three-dimensional overexcavation gap can be accurately calculated by applying the prediction program provided by the invention.

Description

Method for predicting stress field change of surrounding soil body caused by shield tunneling along curved path
Technical Field
The invention belongs to the technical field of shield tunneling and underground engineering, and particularly relates to a method for predicting the change of a stress field of a surrounding soil body caused by tunneling of a shield along a curved path.
Background
When a subway is built, the tunneling path of the shield tunneling machine is not always a straight line segment, and meanwhile, in order to meet the limitation of site conditions, the working condition that the shield tunnels along a curved path is inevitable. In the shield tunnel excavation process, a non-uniform gap exists between the outer wall of the shield tail segment lining at the moment of void and a boundary soil layer; especially for curved tunnels, in order to enable the shield tunneling machine to smoothly tunnel, an overbreak gap on the inner side of a curve is difficult to avoid in the construction process. In the construction process, a clearance caused by curve section overbreak inevitably causes disturbance to surrounding strata, the calculation object of the prediction program of the shield tunneling to the stratum disturbance is a linear tunnel at present, and the calculation program of the stratum stress caused by curve tunnels, particularly soil body loss, is rarely reported. More noteworthy, the prediction of the formation disturbance caused by shield tunneling is mostly limited to the influence of the shield tunneling on the soil displacement, and a few calculation programs or methods capable of predicting the influence of the shield tunneling on the formation stress are available, and the change of the stress state is the main cause of the formation displacement, so that a convenient, fast and reliable calculation program is urgently sought for predicting the change of the stress field of the surrounding soil caused by shield tunneling along a curved path.
Disclosure of Invention
The invention aims to provide a method for predicting the change of the stress field of the surrounding soil body caused by the tunneling of the shield along the curved path, which takes the tunneling of the curved path as an example, and utilizes a calculation program of the change of the stress field of the surrounding soil body along the axial direction and the direction of the annular excavation surface caused by the actual stratum loss amount when the development shield tunnels along the curved path to obtain the stratum stress changed along the axial direction and the stratum stress changed along the annular excavation surface when the development shield tunnels along the curved path.
The purpose of the invention is realized by the following technical scheme:
a method for predicting the stress field change of the surrounding soil body caused by the shield tunneling along a curved path is characterized by comprising the following steps:
(1) obtaining a stress increment solution of any point in space caused by a unit volume gap in a semi-infinite body by using a three-dimensional source-sink method principle;
(2) determining the stratum loss amount during the actual tunneling period according to the tunneling characteristic of the shield along the curved path;
(3) and developing a calculation program of the change of the stress field of the surrounding soil body along the axial direction and the direction of the annular excavation surface caused by the actual stratum loss amount when the shield tunnels along the curved path so as to obtain the stratum stress changed along the axial direction and the stratum stress changed along the annular excavation surface when the shield tunnels along the curved path.
1. The method for predicting the stress field change of the surrounding soil body caused by the shield tunneling along the curved path according to claim 1, wherein the step (1) comprises the following steps:
(1.1) assuming the soil mass as an infinite body without boundaries, the midpoint F (x) of the infinite body is given0,y0,z0) A displacement component S at a unit volume void initiation point P (x, y, z)k1：
Figure BDA0003409838250000021
In the formula:
k is a function argument and is x or y or z;
(k–k0)＝(x–x0)、(y–y0)、(z–z0) One of (1);
r1＝[(x-x0)2+(y-y0)2+(z-z0)2]1/2；
(1.2) obtaining a point F (x)0,y0,z0) Mirror image position point F' (x)0,y0,–z0) Displacement component at point P (x, y, z) of equal volume expansion:
Figure BDA0003409838250000022
in the formula:
m is x or y;
(m–m0)＝(x–x0) Or (y-y)0)；
r2＝[(x-x0)2+(y-y0)2+(z+z0)2]1/2；
(1.3) obtaining the solutions of the strain and the stress generated in the step (1.1) and the step (1.2) by knowing an elastic mechanics basic equation:
Figure BDA0003409838250000023
Figure BDA0003409838250000024
in the formula:
k is a function argument and is x or y or z;
Sk2reference Sm2The calculation formula of (2);
m ═ x, or y;
g is the shear modulus of the soil body;
mu is the soil poisson ratio;
(1.4) obtaining the above two steps results in a stress calculation program along the m-axis direction:
Figure BDA0003409838250000031
wherein:
the m-axis refers to the x-axis or the y-axis;
(m, n) ═ x, y, or (y, x);
the two steps are solutions of stress components of any point caused by gaps and mirror image gaps in the infinite body, and in order to meet the actual boundary condition, namely the semi-infinite condition, the shear stress (G gamma) generated on the earth surface by the first two steps is requiredxz；Gγyz) The stress component generated by the reverse action on the earth surface can be obtained:
Figure BDA0003409838250000032
Figure BDA0003409838250000033
in the formula:
b. c, u and t are all function independent variables;
r3＝[(x-u)2+(y-t)2+z2]1/2；
the sum of the solutions obtained in the above 3 steps is the solution of the stress increment of any point caused by the gap with the radius of 1, so that the stress increment generated by the gap with the unit volume is as follows:
Figure BDA0003409838250000034
(m ═ x or y).
The step (2) comprises the following steps: in order to meet the purpose of turning of a curve section, the inner side of the curve needs to be overetched when the shield is in yawing propulsion, the body of the shield is divided into a front shield and a rear shield by assuming the existence of a hinge device of the shield, the overexcavation amount of the curve section meets the requirement that the tail of the shield covers 2 ring pipe pieces, and the ring width of each pipe piece is b1Meanwhile, considering the timely support of the excavated rear shield, the displacement of the soil body is subjected to three-dimensional constraint, so that the over-excavation amount of the excavated surface is reduced, and 1/3 is obtained according to experienceAnd then, the calculation formula of the overexcavation gap omega of the excavation surface is as follows:
Figure BDA0003409838250000041
in the formula:
q is the curvature radius of the axis of the curved tunnel;
r is the outer diameter of the shield;
b1the ring width of the segment.
The step (3) comprises the following steps: under the influence of curve overbreak, the stress increment caused by the surrounding soil body is calculated by the following steps:
Figure BDA0003409838250000042
in the formula:
theta is the center of a circle of the cross section of the curved tunnel, the included angle between the connecting line of the projection points of the center of the cross section of the curved tunnel on the z axis and the oxz plane in the three-dimensional rectangular coordinate system;
q is a function argument;
l is the tunneling length of the shield;
h is the tunnel axis burial depth.
The method for representing the three-dimensional space distribution of the stress field around the tunnel comprises the following steps: assuming that the tunneling axis of the curve tunnel is a section of circular arc with the radius of Q in the horizontal plane, the selected calculation path is as follows: on one hand, in the horizontal plane of the curve tunnel driving axis, a section of curve which is concentric with the curve tunnel driving axis and is a circular arc is taken as a calculation path, and the radial distance r between the two curves0Is nR, wherein n is 2, 3, 4, …; the calculation path is positioned outside the curve tunnel; on the other hand, a specific section is selected along the curve tunnel tunneling axis, the intersection point of the specific section and the curve tunnel tunneling axis is used as the center of a circle, a circle is drawn on the specific section, and the radius r0-nR, wherein n is 2, 3, 4, …; calculating the difference r0In this case, the stress field at each point of the circumference is distributed circumferentially.
The invention has the advantages that: compared with the prior art, the method is suitable for the working condition that the soil body loss gap is a three-dimensional space, taking tunneling along a curve path as an example, curve overexcavation is needed during construction, and the change of the stress field of the surrounding soil body caused by the three-dimensional overexcavation gap can be accurately calculated by applying the prediction program.
Drawings
FIG. 1 is a flow chart of the prediction of the change of the stress field of the surrounding soil body caused by the shield tunneling along a curved path in the invention;
fig. 2 is a schematic diagram of a curve shield tunneling model and a calculation path in the invention.
Detailed Description
The features of the present invention and other related features are described in further detail below by way of example in conjunction with the following drawings to facilitate understanding by those skilled in the art:
example (b):
as shown in fig. 1, a schematic diagram of a curve shield tunneling model and a calculated path is shown, assuming that a curve tunneling axis is a section of arc with a radius Q in a horizontal plane, the selected calculated path is as follows: on the one hand, in the horizontal plane of the curve tunnel axis, a curve which is concentric with the tunnel axis is taken as a calculation path (hereinafter referred to as the axis direction), and the radial distance r of the two curves0With nR (n ═ 2, 3, 4, …), the calculated path is outside the curvilinear tunnel. On the other hand, a specific section is selected along the tunnel axis, the intersection point of the specific section and the tunnel axis is used as the center of a circle, a circle is drawn on the section, and different r is calculated0In this case, the stress field at each point of the circumference is distributed circumferentially.
As shown in fig. 1 and 2, the embodiment specifically relates to a method for predicting the change of a stress field of a surrounding soil body caused by the fact that a shield tunnels along a curved path, which comprises the following steps:
(1) by applying the three-dimensional source-sink principle, the stress increment solution of any point in space caused by unit volume gap in semi-infinite body is obtained, specifically:
(1.1) assuming that the soil is an infinite body without boundaries, a midpoint F (x) of the infinite body is given0,y0,z0) OfDisplacement component S at unit volume void initiation point P (x, y, z)k1：
Figure BDA0003409838250000051
In the formula:
k is a function argument and is x or y or z;
(k–k0)＝(x–x0)、(y–y0)、(z–z0) One of (1);
r1＝[(x-x0)2+(y-y0)2+(z-z0)2]1/2。
(1.2) obtaining a point F (x)0,y0,z0) Mirror image position point F' (x)0,y0,–z0) Displacement component at point P (x, y, z) of equal volume expansion:
Figure BDA0003409838250000052
in the formula:
m is x or y; it should be noted that, in order to omit various expressions of the formula, the aforementioned letter k is used to represent x, y or z, and m herein represents x or y;
(m–m0)＝(x–x0) Or (y-y)0)；
r2＝[(x-x0)2+(y-y0)2+(z+z0)2]1/2。
(1.3) obtaining the solutions of the strain and the stress generated in the step (1.1) and the step (1.2) by knowing an elastic mechanics basic equation:
Figure BDA0003409838250000061
Figure BDA0003409838250000062
in the formula:
k is a function argument and is x or y or z;
Sk2reference Sm2The calculation formula of (2);
m ═ x, or y;
g is the shear modulus of the soil body;
mu is the soil Poisson's ratio.
(1.4) obtaining the above two steps results in a stress calculation program along the m-axis direction:
Figure BDA0003409838250000063
wherein:
the m-axis refers to the x-axis or the y-axis;
(m, n) ═ x, y, or (y, x);
the two steps are solutions of stress components of any point caused by gaps and mirror image gaps in an infinite body, and in order to meet the actual boundary condition, namely the semi-infinite condition, the shear stress (G gamma) generated on the earth surface by the first two steps is requiredxz；Gγyz) The stress component generated by the reverse action on the earth surface can be obtained:
Figure BDA0003409838250000071
Figure BDA0003409838250000072
in the formula:
b. c, u and t are all function independent variables;
r3＝[(x-u)2+(y-t)2+z2]1/2；
the sum of the solutions obtained in the above 3 steps is the solution of the stress increment of any point caused by the gap with the radius of 1, so that the stress increment generated by the gap with the unit volume is as follows:
Figure BDA0003409838250000073
(m ═ x, or y).
(2) According to the characteristic that the shield tunnels along a curved path, determining the stratum loss amount during the actual tunneling period, specifically:
in order to meet the purpose of turning of a curve segment, the inner side of the curve needs to be overetched when the shield is in yawing propulsion, if the body of the shield is divided into a front shield and a rear shield by the aid of a hinging device of the shield, the overexcavation amount of the curve segment meets the requirement that the tail of the shield covers 2 ring pipe pieces, and the ring width of each pipe piece is b1Meanwhile, considering timely supporting of the excavated rear shield, the displacement of the soil body is subjected to three-dimensional constraint, so that the overexcavation amount of the excavated surface is reduced, 1/3 is obtained according to experience, and the calculation formula of the overexcavation gap omega of the excavated surface is as follows:
Figure BDA0003409838250000074
in the formula:
q is the curvature radius of the axis of the curved tunnel;
r is the outer diameter of the shield;
b1the ring width of the segment.
The program theoretical basis for predicting the change of the stress field of the surrounding soil body caused by the shield tunneling along the curve path is solid, the budget program of the soil body stress caused by the curve overexcavation gap during the construction of the curve shield tunnel is researched, and the calculation is more convenient, rapid and reliable by combining the actual three-dimensional space characteristic of the curve tunnel.
In the tunneling process of the curve shield tunnel, the tunnel line trend determines the complexity of soil loss three-dimensional space, and the stress change of the soil around the curve tunnel is easily caused, so that certain influence is brought to the construction. Therefore, it is necessary to estimate the influence of the actual overbreak clearance on the soil stress in advance according to the actual overbreak clearance value. Please refer to fig. 2, which is a flowchart illustrating a procedure for predicting soil stress around a curved tunnel caused by a curved overexcavation gap according to this embodiment.
(3) Developing a calculation program of the change of a stress field of a surrounding soil body along the axial direction and the direction of an annular excavation surface caused by the loss of an actual stratum when the shield tunnels along a curved path so as to obtain the stratum stress changed along the axial direction and the stratum stress changed along the annular excavation surface when the shield tunnels along the curved path, specifically:
by applying the triple integral principle, the stress increment caused by the surrounding soil under the influence of curve overexcavation can be obtained by the following calculation procedures:
Figure BDA0003409838250000081
in the formula:
theta is the center of a circle of the cross section of the curved tunnel, the included angle between the connecting line of the projection points of the center of the cross section of the curved tunnel on the z axis and the oxz plane in the three-dimensional rectangular coordinate system;
q is a function argument;
l is the tunneling length of the shield;
h is the tunnel axis burial depth.
Compared with the prior art, the program for predicting the stress field change of the surrounding soil body caused by the shield tunneling along the curved path is based on the three-dimensional source-sink principle and the triple integral principle, is combined with the actual three-dimensional space position of the overbreak gap, can accurately predict the stratum additional stress, and has the advantages of high calculation efficiency, easiness in value taking of corresponding parameters, accordance with engineering practice and the like.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.

Claims (5)

1. A method for predicting the stress field change of the surrounding soil body caused by the shield tunneling along a curved path is characterized by comprising the following steps:
(1) obtaining a stress increment solution of any point in space caused by a unit volume gap in a semi-infinite body by using a three-dimensional source-sink method principle;
(2) determining the stratum loss amount during the actual tunneling period according to the tunneling characteristic of the shield along the curved path;
(3) and developing a calculation program of the change of the stress field of the surrounding soil body along the axial direction and the direction of the annular excavation surface caused by the actual stratum loss amount when the shield tunnels along the curved path so as to obtain the stratum stress changed along the axial direction and the stratum stress changed along the annular excavation surface when the shield tunnels along the curved path.
2. The method for predicting the stress field change of the surrounding soil body caused by the shield tunneling along the curved path according to claim 1, wherein the step (1) comprises the following steps:
(1.1) assuming the soil mass as an infinite body without boundaries, the midpoint F (x) of the infinite body is given0,y0,z0) A displacement component S at a unit volume void initiation point P (x, y, z)k1：
Figure FDA0003409838240000011
In the formula:
k is a function argument and is x or y or z;
(k–k0)＝(x–x0)、(y–y0)、(z–z0) One of (1);
r1＝[(x-x0)2+(y-y0)2+(z-z0)2]1/2；
(1.2) obtaining a point F (x)0,y0,z0) Mirror image position point F' (x)0,y0,–z0) Displacement component at point P (x, y, z) of equal volume expansion:
Figure FDA0003409838240000012
in the formula:
m is x or y;
(m–m0)＝(x–x0) Or (y-y)0)；
r2＝[(x-x0)2+(y-y0)2+(z+z0)2]1/2；
(1.3) obtaining the solutions of the strain and the stress generated in the step (1.1) and the step (1.2) by knowing an elastic mechanics basic equation:
Figure FDA0003409838240000021
Figure FDA0003409838240000022
in the formula:
k is a function argument and is x or y or z;
Sk2reference Sm2The calculation formula of (2);
m ═ x, or y;
g is the shear modulus of the soil body;
mu is the soil poisson ratio;
(1.4) obtaining the above two steps results in a stress calculation program along the m-axis direction:
Figure FDA0003409838240000023
wherein:
the m-axis refers to the x-axis or the y-axis;
(m, n) ═ x, y, or (y, x);
the two steps are solutions of stress components of any point caused by gaps and mirror image gaps in the infinite body, and in order to meet the actual boundary condition, namely the semi-infinite condition, the shear stress (G gamma) generated on the earth surface by the first two steps is requiredxz；Gγyz) Acting in the opposite directionOn the surface, the stress component generated can be obtained:
Figure FDA0003409838240000024
Figure FDA0003409838240000031
in the formula:
b. c, u and t are all function independent variables;
r3＝[(x-u)2+(y-t)2+z2]1/2；
the sum of the solutions obtained in the above 3 steps is the solution of the stress increment of any point caused by the gap with the radius of 1, so that the stress increment generated by the gap with the unit volume is as follows:
Figure FDA0003409838240000032
3. the method for predicting the stress field change of the surrounding soil body caused by the shield tunneling along the curved path according to claim 2, wherein the step (2) comprises the following steps: in order to meet the purpose of turning of a curve section, the inner side of the curve needs to be overetched when the shield is in yawing propulsion, the body of the shield is divided into a front shield and a rear shield by assuming the existence of a hinge device of the shield, the overexcavation amount of the curve section meets the requirement that the tail of the shield covers 2 ring pipe pieces, and the ring width of each pipe piece is b1Meanwhile, considering timely supporting of the excavated rear shield, the displacement of the soil body is subjected to three-dimensional constraint, so that the overexcavation amount of the excavated surface is reduced, 1/3 is obtained according to experience, and the calculation formula of the overexcavation gap omega of the excavated surface is as follows:
Figure FDA0003409838240000033
in the formula:
q is the curvature radius of the axis of the curved tunnel;
r is the outer diameter of the shield;
b1the ring width of the segment.
4. The method for predicting the stress field change of the surrounding soil body caused by the shield tunneling along the curved path according to claim 3, wherein the step (3) comprises the following steps: under the influence of curve overbreak, the stress increment caused by the surrounding soil body is calculated by the following steps:
Figure FDA0003409838240000034
in the formula:
theta is the center of a circle of the cross section of the curved tunnel, the included angle between the connecting line of the projection points of the center of the cross section of the curved tunnel on the z axis and the oxz plane in the three-dimensional rectangular coordinate system;
q is a function argument;
l is the tunneling length of the shield;
h is the tunnel axis burial depth.
5. The method for predicting the stress field change of the surrounding soil body caused by the shield tunneling along the curved path according to claim 4, wherein the method for representing the three-dimensional space distribution of the stress field around the tunnel comprises the following steps: assuming that the tunneling axis of the curve tunnel is a section of circular arc with the radius of Q in the horizontal plane, the selected calculation path is as follows: on one hand, in the horizontal plane of the curve tunnel driving axis, a section of curve which is concentric with the curve tunnel driving axis and is a circular arc is taken as a calculation path, and the radial distance r between the two curves0Is nR, wherein n is 2, 3, 4, …; the calculation path is positioned outside the curve tunnel; on the other hand, a specific section is selected along the curve tunnel tunneling axis, the intersection point of the specific section and the curve tunnel tunneling axis is used as the center of a circle, a circle is drawn on the specific section, and the radius r0-nR, wherein n is 2, 3, 4, …; calculating the difference r0In the case of the positions of the points on the circumferenceAnd the stress field is distributed annularly.
CN202111524883.2A 2021-12-14 2021-12-14 Method for predicting stress field change of surrounding soil body caused by shield tunneling along curved path Pending CN114417451A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115809500A (en) * 2023-02-06 2023-03-17 北京云庐科技有限公司 Method for determining safety coefficient of excavation surface of multi-soil-layer shield tunnel

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115809500A (en) * 2023-02-06 2023-03-17 北京云庐科技有限公司 Method for determining safety coefficient of excavation surface of multi-soil-layer shield tunnel

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